vvavgavg = Δd/ = Δd/ΔΔtt

aaavgavg = Δv/ = Δv/ΔΔtt

Δd = vΔd = viiΔΔt + .5at + .5aΔΔtt22

vvf f = v= vii + a + aΔΔtt

vvff2 2 = v= vii

22 + 2a + 2aΔΔdd

Sin = Opp/HypSin = Opp/Hyp

Cos = Adj/HypCos = Adj/Hyp

Tan = Opp/AdjTan = Opp/Adj

KinematicsKinematics

KinematicsKinematics

the study of motionthe study of motion

MotionMotion

What does it mean for an What does it mean for an object to be in motion?object to be in motion?

the change in position of an the change in position of an object as compared to a object as compared to a reference point reference point

*

Is the brick wall moving?Is the brick wall moving?

Not from where she’s sitting, but…Not from where she’s sitting, but…

……from space, the earth rotates from space, the earth rotates and the wall with it.and the wall with it.

So, whether or not something is moving depends on your frame of reference. *

Frame of ReferenceFrame of Reference

a fixed point used to determine a fixed point used to determine magnitude and direction of motionmagnitude and direction of motion

Magnitude?Magnitude?

See Video HereSee Video Here

RateRate

a change in a given quantity over a a change in a given quantity over a specified period of time (examples: specified period of time (examples: velocity and acceleration)velocity and acceleration)

Scalar quantityScalar quantity

a measurement specified by a measurement specified by magnitude only. magnitude only.

No direction impliedNo direction implied

Ex. mass, volume, density, distance, Ex. mass, volume, density, distance, speed, temperaturespeed, temperature

Vector quantityVector quantity

a measurement specified by a measurement specified by magnitude and directionmagnitude and direction

Ex.: displacement, velocity, Ex.: displacement, velocity, acceleration, forceacceleration, force

DistanceDistance

the length of the actual path taken the length of the actual path taken by the object regardless of directionby the object regardless of direction

scalar quantityscalar quantity

units include m, kmunits include m, km

DisplacementDisplacement

length (measured in a straight line) length (measured in a straight line) from the reference point to the from the reference point to the object (implies a given direction)object (implies a given direction)

vector quantityvector quantity

units include m, kmunits include m, km

DisplacementDisplacement

Displacement = change in Displacement = change in position = final position – position = final position – initial positioninitial position

Symbolically, dSymbolically, d = d = dff – d – dii

**

Total Displacement

Add individual displacement's indicating individual directions with +/-

Remove following slides

Reference point is origin or start positionWhat is the distance? 70 cmWhat is the displacement? d = df – di

dΔ = 80cm – 10cmdΔ = 70cm

In Centimeters

Reference point is origin or start positionWhat is the distance? 70 cmWhat is the displacement? d = df – di

dΔ = 10cm – 80cmdΔ = -70cm

In Centimeters

Displacement indicates direction. Convention dictates right will be considered positive and left will be considered negative

Reference point is origin or start positionWhat is the distance? 70 mWhat is the displacement? d = df – di

dΔ = 40cm – -30cmdΔ = 70cm

In Centimeters-30 -20 0-10 2010 30 40 50 60

Reference point is origin or start positionWhat is the distance? 70 mWhat is the displacement? d = df – di

dΔ = -30cm – 40cmdΔ = -70cm

In Centimeters-30 -20 0-10 2010 30 40 50 60

Displacement is not always equal to distance travelled! What is Clyde the

Caterpillar’s displacement?d = df – di

d = 80m – 20m = 60m

Home

KCHS

Gas

Mall Movies

1 km

1.75 km

2.0 km

1.5 km

Example ADraw this diagram and determine the following in reference to home:

NORTH

Determine the distance and Determine the distance and displacement for each scenario in displacement for each scenario in

reference to homereference to home1.1. You drive from home to the mall.You drive from home to the mall.

2.2. You drive from home and stop at the gas You drive from home and stop at the gas station. You realize you left your wallet at station. You realize you left your wallet at home. You go back home to get it. You home. You go back home to get it. You stop at gas station then continue on to the stop at gas station then continue on to the mall.mall.

3.3. You drive from the mall to the gas station.You drive from the mall to the gas station.

4.4. You drive from home to school.You drive from home to school.

For total displacement

Add displacement vectors. Sign indicates direction.

1.1. Home-mallHome-mall

Dist = 3.5 km Disp =3.5 km NDist = 3.5 km Disp =3.5 km N

2.2. Home-gas-home-gas-mallHome-gas-home-gas-mall

Dist = 6.5 km Disp =3.5 km NDist = 6.5 km Disp =3.5 km N

3.3. Mall-gasMall-gas

Dist = 2.0 km Dist = 2.0 km

Disp =1.5 km -3.5 km =-2km (you are going Disp =1.5 km -3.5 km =-2km (you are going south) Assuming mall is reference point south) Assuming mall is reference point

4.4. Home-schoolHome-schoolDist = 1.0 km Dist = 1.0 km

Disp =-1.0 km -0 km =-1 km (you are going south)Disp =-1.0 km -0 km =-1 km (you are going south)

9/10Goal: Prepare for Thursday’s testWe will go over the trig quiz and Reading QuizYesterday we discussed scalar and vector quantities. We learned how trig was applied to displacement problems.While waiting for class to start, complete sample problems 1 & 2 in kinematics notes.Pick up 03 WS I. This is due tomorrow.

complete these DA problem:– Your drive your car at 45 mph for a million

kilometers. How many seconds will it take? (1 in= 2.54 cm)

– Convert 98 feet/second to nm/decade. Convert 98 feet/second to nm/decade. Assume 365.25 days = 1 year Assume 365.25 days = 1 year 1 km = 1 km = 0.621 miles 0.621 miles

9/10

Goal: Prepare for Thursday’s testWe will go over the trig quiz and Reading QuizWhile waiting for class to start, complete this DA problem:– Your drive your car at 45 mph for a

million kilometers. How many seconds will it take? (1 in= 2.54 cm)

9/11 We remember……Goal: Prepare for tomorrow’s testHave last night’s homework (03WS1) out to be checked.While waiting for class to start, complete this DA problem:

An otter scampers down Mrs. Sauder’s dock An otter scampers down Mrs. Sauder’s dock for a distance of 23.0 feet. How long does it for a distance of 23.0 feet. How long does it take the otter (in seconds) to get to the end take the otter (in seconds) to get to the end of the dock if its average speed is 1.78 feet/s? of the dock if its average speed is 1.78 feet/s? What is the otter’s rate of speed in m/s? What is the otter’s rate of speed in m/s?

Your drive your car at 45 mph for a million kilometers. How many seconds will it take? (1 in= 2.54 cm)

4.97 x 107 sec

..

1 x 106 km 1000 m 100 cm 1 in1 1 km 1 m 2.54 cm

1 ft 1 mile 1hr 3600 sec

12 in 5280 ft 45 miles 1 hr

Sine, Cosine, Tangent

http://www.mathsisfun.com/sine-http://www.mathsisfun.com/sine-cosine-tangent.htmlcosine-tangent.html

Thursday’s testThursday’s test

3-4 dimensional analysis problems3-4 dimensional analysis problems

1 accuracy vs precision problem1 accuracy vs precision problem

Solving a right triangleSolving a right triangle

2 Linear distance and displacement 2 Linear distance and displacement problemproblem

Right angle distance and displacement Right angle distance and displacement problem where you must determine problem where you must determine the angle in reference to X axis!!! the angle in reference to X axis!!!

Unit 03 WSI1. c = 9.63u (pythagoreans) A = 59.8° (tan) B = 30.2°2. Walk 8yds east…. Dist = 35 yards Disp= -5 yards or 5 yards west3 . Somersaults…. Dist = 10 yards Disp = 7.62 yards at 66.8° S of W4. 30.2 km (start with 45 min)5. 10500 sec (start with 211 km)

Same diagram, last question….Same diagram, last question….

5. You drive from home to the mall and 5. You drive from home to the mall and then to the movies.then to the movies.

Distance?Distance?

5.25 km5.25 km

Displacement?Displacement?

Use Pythagoreans: 3.91kmUse Pythagoreans: 3.91km

How do you indicate direction?How do you indicate direction?

Home

KCHS

Gas

Mall Movies

1 km

1.75 km

2.0 km

1.5 km

The displacement is the dotted line. This is referred to as the resultant.

NORTH

Tests are graded. If you have not taken test, you will take it today during class. Missed benchmarks will be given next M, T, and W after school.You will have until the last ten minutes of class to work on test corrections. This will earn you a daily grade. Expectations: Write out givens, redo all the work. Include appropriate diagrams. For future reference, if it is not a math problem you would write out question and answer.Make sure to include name and period at top of corrections. Staple corrections to test and place in blue sorter.

9/14 Pick up vector sheet

Arrows represent vectorsLength of arrow corresponds to magnitude of vectorConnect the tail of one vector to the arrow tip of the otherNo matter what route you take from point A to point B your final displacement vector will be the sameThe final displacement vector is called the resultant vectorDraw in the resultant vector from the tail of the first vector to the arrow head of the second

Vector Diagrams

Home

KCHS

Gas

Mall Movies

1 km

1.75 km

2.0 km

1.5 km

To determine direction, view diagram on a coordinate plane. Direction is determined in reference to the x axis. This would be angle θ.

NORTH

θ

In reference to XIn reference to X

tan tan θθ = 3.5/1.75 = 3.5/1.75

tan tan θθ = 2 = 2

θθ = 63.4 = 63.4°° North of East North of East

N of E, E of N

I am confused. Which is which?

Complete Displacement practice Complete Displacement practice problems 1&2 in note packet and problems 1&2 in note packet and 1,3, & 4 on WS 011,3, & 4 on WS 01

Solving Problem Set UpsSolving Problem Set Ups

Place givenPlace given

information information

on left.on left.Draw diagramhere ifapplicable.

show formula and substitution here. Box in answer.

Displacement Practice

1. ∆d = +2m or 2m north2. r = 17.7m at 73.6° S of W

9/18 Power up and Go to Tablet Camp 9/18 Power up and Go to Tablet Camp (you downloaded this yesterday) You (you downloaded this yesterday) You will work through one tutorial this period.will work through one tutorial this period.

You are riding in the MS You are riding in the MS 150. Would you rather 150. Would you rather ride into the wind or have ride into the wind or have it at your back??it at your back??

(BTW The MS150 benefits (BTW The MS150 benefits MS and occurs every AprilMS and occurs every April))

What is the difference between What is the difference between speed and velocity?speed and velocity?

SpeedSpeed

change in distance divided by change in distance divided by change in time (d/t )change in time (d/t )

scalar quantityscalar quantity

units include m/sec or cm/sec.units include m/sec or cm/sec.

VelocityVelocity

speed in a given direction speed in a given direction

magnitude and direction included in magnitude and direction included in the measurementthe measurement

vector quantityvector quantity

units include m/sec or cm/sec.units include m/sec or cm/sec.

Average VelocityAverage VelocityThe average velocity of an object is The average velocity of an object is defined as the displacement of an defined as the displacement of an object divided by the time in which it object divided by the time in which it took place.took place.

Average velocity Average velocity = =

vvavgavg = =

Change in displacement

Change in time

dt

**

AbbreviationsAbbreviations

Example BExample B

A motorcycle drives 825m east in 1.4 A motorcycle drives 825m east in 1.4 min. What is its average velocity in min. What is its average velocity in km/hr? If the biker was driving km/hr? If the biker was driving through a school zone (20 mph limit) through a school zone (20 mph limit) should she be ticketed?should she be ticketed?

You can solve this without any You can solve this without any knowledge of velocity by using knowledge of velocity by using dimensional analysis and following dimensional analysis and following the units.the units.

Example BExample B

A motorcycle drives 825m east in A motorcycle drives 825m east in 1.4 min. What is its average 1.4 min. What is its average velocity in km/hr? If the biker velocity in km/hr? If the biker was driving through a school was driving through a school zone (20 mph limit) should she zone (20 mph limit) should she be ticketed?be ticketed?

35.4 km/h35.4 km/h

22.0 mph yes22.0 mph yes

Example CExample C

What distance (in km) does a What distance (in km) does a helicopter travel in 39.7 minutes helicopter travel in 39.7 minutes provided it moves in a direct provided it moves in a direct path at 25.8 m/s?path at 25.8 m/s?

You can solve this without any You can solve this without any knowledge of velocity by using knowledge of velocity by using dimensional analysis and dimensional analysis and following the units.following the units.

Example CExample C

What distance (in km) does a What distance (in km) does a helicopter travel in 39.7 minutes helicopter travel in 39.7 minutes provided it moves in a direct provided it moves in a direct path at 25.8 m/s?path at 25.8 m/s?

61.5 km61.5 km

Work through examples D-F Work through examples D-F showing velocity as a vectorshowing velocity as a vector

Remember v = Remember v = dd

tt

Solving Problem Set UpsSolving Problem Set Ups

Place givenPlace given

information information

on left.on left.Draw diagramhere ifapplicable.

show formula and substitution here. Box in answer.

A plane heading east at 632 A plane heading east at 632 miles per hour is directly hit by a miles per hour is directly hit by a wind measuring 25 miles per wind measuring 25 miles per hour. The wind is blowing hour. The wind is blowing directly west. Without directly west. Without correction, what is the plane’s correction, what is the plane’s resultant velocity?resultant velocity?

Example D

+632 mph-25 mph = +607mph+632 mph-25 mph = +607mph

Indicate direction with + or –Indicate direction with + or –

East, North, or Right +East, North, or Right +

West, South, or Left -West, South, or Left -

+632 mph

-25 mph

Example EExample E

Later in its journey, the wind Later in its journey, the wind shifts to the north. The plane, shifts to the north. The plane, heading east at 632 miles per heading east at 632 miles per hour, is hit by this 25-mph wind. hour, is hit by this 25-mph wind. Without correction, what is the Without correction, what is the plane’s resultant velocity?plane’s resultant velocity?

How do we figure out the resultant How do we figure out the resultant velocity?velocity?

You guessed it! A triangle!You guessed it! A triangle!

The resultant velocity vector is c. Use The resultant velocity vector is c. Use Pythagoreans to solve just as you did Pythagoreans to solve just as you did with displacement.with displacement.

Then solve for direction in reference to Then solve for direction in reference to the x axis. Do you know which angle?the x axis. Do you know which angle?

632 mph E

25 mph Nc

θ

c = 632 mph (632.4942….) c = 632 mph (632.4942….)

Did you really expect a measly 25 Did you really expect a measly 25 mph north wind to affect the plane’s mph north wind to affect the plane’s eastern velocity?eastern velocity?

tantanθθ =2.27 =2.27° ° N of E N of E

632 mph E

25 mph Nc

θ

What if I made my diagram like What if I made my diagram like this?this?

It doesn’t matter, you get all the It doesn’t matter, you get all the same answers.same answers.

632 mph E

25 mph N

θ

Example F You are on a 32 ft boat. The boat is moving northward at 0.8m/s. You walk from stern to bow at 0.2m/s.

A. How long did it take you (in seconds) to walk the entire

length of the boat? (1in = 2.54 cm).

Example F continued….You are on a 32 ft boat. The boat is moving northward at 0.8m/s. You walk from stern to bow at 0.2m/s.

B. What is the magnitude and

direction of your apparent resulting velocity in reference to the earth?

Example FExample FPart APart A

You want sec. What to start with?You want sec. What to start with?

32 ft: Use dimensional analysis.32 ft: Use dimensional analysis.

Ft-in-cm-m-sec!Ft-in-cm-m-sec!

t = 48.8 sect = 48.8 sec

Part BPart B

Solve for vSolve for vrr

++0.2m/s + 0.2m/s + ++0.8 m/s = 1.0 m/s N0.8 m/s = 1.0 m/s N

Skip Example G

A plane is headed 25.8° west of northat 340mi/hr when the wind is from thesouth at 45mi/hr. What is theapparent resultant velocity of the plane with respect to the ground?

9/19Today we will look at more complex motion problems. We will discuss D, E, and F if not discussed yesterday.Have a calculator and pick up Unit 03 WSIII ABegin working on WS III A while waiting for class to start. Please do on paper.Today (after school) is last for completing test corrections and retakes.

9/20

Today we will continue the girl scout problem. Have HW from yesterday ready to be checked. (Unit 03 WSIII A)Pick up WS III B and a calculator.Quiz tomorrow over resolving vectors at right angles and girl scout type problem.Yesterday (after school) was last day for completing test corrections and retakes.

??????????

Maybe introduce walking across a Maybe introduce walking across a boat as it is movingboat as it is moving

Example HExample HA girl scout elects to swim across the A girl scout elects to swim across the river. The river is 37.5 meters wide. A river. The river is 37.5 meters wide. A current flows downstream at a rate of current flows downstream at a rate of 0.66 m/s. If she initially swims towards 0.66 m/s. If she initially swims towards the boy scout camp (directly cross the the boy scout camp (directly cross the river) at a rate of 1.73 m/s, how long will river) at a rate of 1.73 m/s, how long will it take her to reach the far shore?it take her to reach the far shore?

Remember what the question asks. Remember what the question asks.

How long does it take her to swim across? How long does it take her to swim across?

To solve for time, what do we need to To solve for time, what do we need to know?know?

Use velocity and displacement but only in Use velocity and displacement but only in reference to crossing the river.reference to crossing the river.

] 37.5m

1.73 m/s

v = d/t v = d/t

t = d/v t = d/v

t = 37.5m÷1.73m/s t = 37.5m÷1.73m/s

t = 21.7 st = 21.7 s

] 37.5m

1.73 m/s

Where exactly does the girl scout Where exactly does the girl scout end up on the far shore?end up on the far shore?

What do we need to know?What do we need to know?

To determine displacement we To determine displacement we need velocity and time but only in need velocity and time but only in reference to downstream.reference to downstream.

] 37.5m

1.73 m/s

Example I

To find where she ends up, what is the To find where she ends up, what is the downstream velocity?downstream velocity?

0.66m/s0.66m/s

What is the time?What is the time?

21.7 sec21.7 sec

Time is the same for both cross stream and Time is the same for both cross stream and downstream.downstream.

14.3 m downstream14.3 m downstream

0.66m/s

When working with multiple vectors When working with multiple vectors remember they are independent of remember they are independent of one another although they have a one another although they have a net effect.net effect.

In the case of the girl scout, her In the case of the girl scout, her overall (think resultant) velocity and overall (think resultant) velocity and direction changed.direction changed.

Do you know how to solve for the Do you know how to solve for the apparent resultant velocity and apparent resultant velocity and direction?direction?

Resultant velocity?Resultant velocity?

cc22 = 1.73 = 1.7322 + 0.66 + 0.6622

c = 1.85 m/sc = 1.85 m/s

Which angle for direction?Which angle for direction?

tan tan θθ = 1.73/0.66 = 2.62… = 1.73/0.66 = 2.62…

θθ = 69.1 = 69.1°

vvrr = 1.85 m/s at 69.1 = 1.85 m/s at 69.1° downstream in respect to downstream in respect to shoreshore

0.66m/s

1.73 m/s c

θ

What angle should the What angle should the girl scout enter the girl scout enter the water upstream to end water upstream to end up at the boy scout up at the boy scout camp??camp??

69.169.1° upstream in pstream in respect to shorerespect to shore

0.66m/s

1.73 m/s c

θ

9/21Get a calculator. You must you my calculator for the quiz. Make sure it is degree mode.Have homework out to be checkedWe will go over problems 1 and 2. Then we will take quiz.After quiz we will discuss 3-5

IT’S FRIDAY!!!!!

9/24 Tutoring M,T, W after schoolGet a calculator and formula sheetThe quizzes from FRIDAY are graded. See me to make up. Remember we have a test on WedHW: kinematics WS V 1-8 (See LMS)Today’s goal: apply acceleration formulas to motion. Open kinematics notes on LMS. Go to III B: Acceleration

What is the westerly What is the westerly component?component?

What is the northerly What is the northerly component?component?

What does c represent?What does c represent?

What can we say about What can we say about the units?the units?

A

B c

θ

#5 610 km/hr East792 km/hr North1590 km E2060 km N

If you are driving is your speed If you are driving is your speed always the same?always the same?

There are a variety of formulas There are a variety of formulas that are used to calculate how that are used to calculate how the position of an object the position of an object changes.changes.

Be prepared: You are going to Be prepared: You are going to be algebraically challenged!!!!!be algebraically challenged!!!!!

How do we define average How do we define average velocity?velocity?

Change in displacement divided Change in displacement divided by change in timeby change in time

What is the formula?What is the formula?

vvavgavg = Δd/ = Δd/ΔΔtt

Algebraically we can come up Algebraically we can come up with the following….with the following….

vvavgavg = (v = (vii + v + vff)/2)/2

Δd/Δd/ΔΔt = (vt = (vii + v + vff)/2)/2

2Δd = (v2Δd = (vii + v + vff))ΔΔtt

Δd = ½ (vΔd = ½ (vii + v + vff))ΔΔtt

If it is yellow, it probably is important. If it is yellow, it probably is important.

This is the mother equation for the This is the mother equation for the 3 big acceleration formulas.3 big acceleration formulas.

How do we define average How do we define average acceleration?acceleration?

Change in velocity divided by Change in velocity divided by change in timechange in time

What is the formula?What is the formula?

aaavgavg = Δv/ = Δv/ΔΔtt

With a little algebra, this can be With a little algebra, this can be rewritten asrewritten as

aaavgavg = Δv/ = Δv/ΔΔtt

aaavgavg = (v = (vff - v - vii)/(t)/(tff – t – tii))

vvf f = v= vii + a + aΔΔtt

What else can we come up What else can we come up with?with?

Δd = ½ (vΔd = ½ (vii + v + vff))ΔΔtt

Δd = ½ (vΔd = ½ (vii +[v +[vi i + a+ aΔΔt]t]ΔΔtt

Δd = ½ (2vΔd = ½ (2vii + a + aΔΔt)t)ΔΔtt

Δd = vΔd = viiΔΔt + ½at + ½aΔΔtt22

Anything else?Anything else?

Δd = ½ (vΔd = ½ (vii + v + vff))ΔΔtt

2Δd = (v2Δd = (vii + v + vff))ΔΔtt

Δt = 2Δd/(vΔt = 2Δd/(vii + v + vff))

vvf f =v=vii + a + aΔΔtt

vvf f =v=vii + a[(2 + a[(2ΔΔd)/(vd)/(vii + v + vff)])]

Continuing….Continuing….

Continuing…..Continuing…..

vvf f =v=vii + a[(2 + a[(2ΔΔd)/(vd)/(vii + v + vff)])]

(v(vii - v - vff) = [(2a) = [(2a Δ Δd)/(vd)/(vii + v + vff)])]

(v(vii - v - vff)(v)(vii + v + vff) = 2a) = 2a Δ Δdd

vvf f vvii – v – viivvff – v – vii22 + v + vff

22 = 2a= 2aΔΔdd

vvff2 2 = v= vii

22 + 2a + 2aΔΔdd

For next year: Rewrite formulas to mimic Starr chart

What 3 major equations will What 3 major equations will we be working with?we be working with?

Δd =Δd =

vvf f ==

vvff2 2 ==

What 3 major equations will What 3 major equations will we be working with?we be working with?

Δd = vΔd = viiΔΔt + ½at + ½aΔΔtt22

vvf f = v= vii + a + aΔΔtt

vvff2 2 = v= vii

22 + 2a + 2aΔΔdd

vvf f = v= vii + a + aΔΔtt– Solve for tSolve for t

vvff2 2 = v= vii

22 + 2a + 2aΔΔdd– Solve for dSolve for d

Horizontal accelerationproblems

Example JA tricycle, initially traveling at 0.15 m/s, experiences an acceleration of 0.045 m/s2. What is the velocity of such tricycle after a period of 15 seconds?

Example Jvi = 0.15 m/s

a = 0.045 m/s2

t = 15 svf = ?

What equation?vvff = v = vii + a + aΔΔttvvff = = 0.15 m/s +( 0.045 m/s2)(15 s)vf = 0.83 m/s

Example KA bowling ball decelerates. If it slows

from 15.3 m/s to 2.77 m/s in 14.0 seconds, what is the measure of such deceleration?

Example Kvi = 15.3 m/s

vf = 2.77 m/s

t = 14.0 sa = ?

What equation?vvff = v = vii + a + aΔΔttSolve for aSolve for avvff = v = vii + a + aΔΔttvvff - v - vii = a = aΔΔtt(v(vff – v – vii)/)/ΔΔt = at = a

a = (2.77 m/sa = (2.77 m/s – 15.3 m/s)/(14.0 s)a= -0.895 m/s2

Example LAn arrow takes a horizontal path for a

distance of 280 m. The arrow slows from 26.3 m/s to 15 m/s during flight. How long does it take for this arrow to fly this distance?

Example L

vi = 26.3 m/s

vf = 15 m/s

d = 280 mt = ?

What equation?This will need 2 different equations! We will solve for a then t

vvff22 = v = vii

22 + 2a + 2aΔΔddSolve for aSolve for a

vvff22 = v = vii

22 + 2a + 2aΔΔddvvff

22 – v – vii22 = 2a = 2aΔΔdd

(v(vff22 – v – vii

22)/2)/2ΔΔd = ad = aa = (15 m/s)a = (15 m/s)22-(26.3-(26.3m/s)2/(2 x 280m)a= -0.83 m/s2

Example L part 2

vi = 26.3 m/s

vf = 15 m/s x = 280 ma = 0.83 m/s2

t = ?

What is the 2nd equation?vvff = v = vii + a + aΔΔttSolve for tSolve for tvvff - v - vii = a = aΔΔtt(v(vff – v – vii)/a)/a = = ΔΔttΔΔt = (15 m/s-26.3 t = (15 m/s-26.3 m/s)/-0.83 m/s2

ΔΔt = 14 st = 14 s

9/24 Tutoring M,T, W after school

Get a calculatorThe quizzes from FRIDAY are graded. I will be passing them back today. Remember we have a test on WedHave out HW: kinematics WS V 1-8Today’s goal: review acceleration formulas to motion. For future reference, download HW assignments in class so you don’t have to worry about connectivity at home.

Write in 3 SF and proper Write in 3 SF and proper Scientific NotationScientific Notation

436,700436,700

36023602

0.0000058000.000005800

402,400,002402,400,002

0.04333333330.0433333333

Write in 3 SF and proper Write in 3 SF and proper Scientific NotationScientific Notation

436,700 436,700 4.37 x 104.37 x 1055

36023602 3.60 x 103.60 x 1033

0.0000058000.000005800 5.80 x 105.80 x 10-6-6

402,400,002402,400,002 4.02 x 104.02 x 1088

0.04333333330.0433333333 4.33 x 104.33 x 10-2-2

Meter Stick LabMeter Stick LabPart IPart I

DO THIS NOW : ) DO THIS NOW : ) On new page in Lab Book, On new page in Lab Book, Title a page: Meter Stick Lab.Title a page: Meter Stick Lab.

There is a blue card on the desks.There is a blue card on the desks.

Determine length in cm and convert to Determine length in cm and convert to meters. Remember to estimate one value meters. Remember to estimate one value beyond smallest interval. Thus your beyond smallest interval. Thus your measurement should be xx.xx cm Record measurement should be xx.xx cm Record length of card in lab booklength of card in lab book

DO NOT WRITE THE MEASUREMENT ON THE DO NOT WRITE THE MEASUREMENT ON THE BLUE CARD!!!!!!!BLUE CARD!!!!!!!

9/27 Tutoring M,T, W after schoolGET YOUR LAB BOOKS!!!!

Yesterday we took the kinematics test. If you were absent, make ups are on Monday after school. Test corrections will be offered Monday and Wednesday after school next week. I will not be available next Tuesday after school.For future reference, download HW assignments in class so you don’t have to worry about connectivity at home.

Meter Stick LabMeter Stick LabPart IPart I

Dollar Bill BetDollar Bill Bet

Without trying to catch the Without trying to catch the falling dollar bill, hypothesize if falling dollar bill, hypothesize if you can catch it before it falls you can catch it before it falls through your fingers.through your fingers.

TEACHER NOTESTEACHER NOTES

Describe the bet about catching a Describe the bet about catching a dollar billdollar bill

Have students measure a dollar bill Have students measure a dollar bill in cm and convert to m (I have some in cm and convert to m (I have some cardboard ones)cardboard ones)

Meter Stick LabMeter Stick LabPart IPart I

Why do objects fall?Why do objects fall?

What factors influence the rate of a What factors influence the rate of a falling object?falling object?

Assume in the following experiment that Assume in the following experiment that air resistance is negligible and that air resistance is negligible and that objects will accelerate downward at a objects will accelerate downward at a uniform rate of 9.8 m/suniform rate of 9.8 m/s22

Gravity in a Vacuum

This video is 3 min and 41 secondsThis video is 3 min and 41 seconds

If the link does not work, the name is If the link does not work, the name is The Mechanical Universe: The Law of Falling Bodies

Show segment Gravity in a vacuumShow segment Gravity in a vacuum

Free FallFree Fall

In the absence of air resistance In the absence of air resistance all objects dropped near the all objects dropped near the surface of a planet fall with the surface of a planet fall with the same constant acceleration.same constant acceleration.

Such motion is referred to as Such motion is referred to as free fallfree fall..

Acceleration due to GravityAcceleration due to GravityFree fall acceleration—aka called Free fall acceleration—aka called acceleration due to gravityacceleration due to gravity

denoted with the symbol denoted with the symbol g or ag or agg..

Down is positive since it is natural Down is positive since it is natural to fall downto fall down

g = g = aagg = 9.80m/s = 9.80m/s22

Meter Stick Lab Part IIMeter Stick Lab Part IIObjective Objective

Use acceleration of gravity to determine your Use acceleration of gravity to determine your

reaction time.reaction time.

Materials Materials Meter StickMeter Stick

MethodsMethods 1.1.Prepare a table in your lab book to record Prepare a table in your lab book to record

distance of catch in centimeters. Remember to distance of catch in centimeters. Remember to give the table a title and to label columns.give the table a title and to label columns.

2.2.Drop and catch the meter stick. Remember to Drop and catch the meter stick. Remember to start at zero. Perform 5 trials.start at zero. Perform 5 trials.

3.3.Average 5 individual trials . Convert average Average 5 individual trials . Convert average cm to meters using dimensional analysis.cm to meters using dimensional analysis.

Meter Stick Lab Part IIMeter Stick Lab Part II4. Reevaluate your hypothesis concerning the 4. Reevaluate your hypothesis concerning the

dollar bill. Would you win the bet? Make a dollar bill. Would you win the bet? Make a statement and justify your answer.statement and justify your answer.

5. Refer to your acceleration formulas and use 5. Refer to your acceleration formulas and use your data to calculate your reaction time. your data to calculate your reaction time. Hint: list your knowns (d-v-v-a-t)Hint: list your knowns (d-v-v-a-t)

6. Show formula used, rearranged, substitution, 6. Show formula used, rearranged, substitution, and answer beneath your data table.and answer beneath your data table.

7. Δd = v7. Δd = viiΔΔt + ½at + ½aΔΔtt22

What is the value for vWhat is the value for viiΔΔtt ? ? Record your reaction time in 3 SFRecord your reaction time in 3 SF

What is your reaction time What is your reaction time related to?related to?

Meter Stick Lab Part IIIMeter Stick Lab Part IIIObjective Objective Use your reaction time to Use your reaction time to determine motor nerve conduction speed.determine motor nerve conduction speed.

• What 2 values do you need for speed?What 2 values do you need for speed?• Assume that the impulse in the motor Assume that the impulse in the motor

neuron traveled from the back of your head neuron traveled from the back of your head to the tip of your index finger. Thus, to the tip of your index finger. Thus, measure this distance to find d. What units measure this distance to find d. What units should you use to record this distance?should you use to record this distance?

• Solve for velocity of the impulse using Solve for velocity of the impulse using your reaction time and distance from index your reaction time and distance from index finger to back of head. Show formula, finger to back of head. Show formula, substitution, and answer.substitution, and answer.

MY DATAMY DATA

Dollar bill 15.50 cm = .155mDollar bill 15.50 cm = .155m

Average of 5 catches 32.40 cm = .324 mAverage of 5 catches 32.40 cm = .324 m

Time to catch 0.257 secTime to catch 0.257 sec

Distance from finger tip to base of skullDistance from finger tip to base of skull 84.50 cm84.50 cm

9/28Goals: Apply acceleration formulas to vertical problemsYesterday we performed the meter stick lab. You can make this up today after school, next Monday or Tuesday morning, or Monday or Wednesday afternoon. Have kinematics notes open to Example M. HW: Unit 03WS VI. We will start this in class today. Upload it now. This will be due Tuesday. Work on #1 and #2 while waiting for class to start.

A boy is spinning on a merry-go-round A boy is spinning on a merry-go-round at constant speed of 0.5 m/s. Describe at constant speed of 0.5 m/s. Describe his velocity. Describe his acceleration.his velocity. Describe his acceleration.

v=d/t or the big 3??Only use v=d/t when you have an average

velocity given or asked for

If objects are starting, stopping, or changing speed, then you must use the big 3

#1 3.3 s#2 -5 m/s2

Example MExample MA villain from a “007” movie is dropped from A villain from a “007” movie is dropped from

a plane flying 0.470 km above the ground. a plane flying 0.470 km above the ground.

A. Without the antagonistic effects of a A. Without the antagonistic effects of a parachute and air resistance, determine parachute and air resistance, determine the acceleration of this individual as he the acceleration of this individual as he plummets to the ground. plummets to the ground.

B.B. With what velocity does this person hit With what velocity does this person hit the ground? the ground?

C.C. How long will it take for this person to How long will it take for this person to meet his demise? meet his demise?

Example MExample MDetermine the accelerationDetermine the acceleration

The acceleration = 9.80m/s9.80m/s22

Example MExample MDetermine the Determine the vf

List your knowns: d = 0.470 km

vi = 0 m/s

vf = ?

a = 9.80m/s9.80m/s22 t = ? Choose the appropriate formula and Solve

for vf

Example MExample M Determine the Determine the vf

vvff22 = v = vii

22 + 2a + 2aΔΔdd

vvff22 = ( = (0 m/s)2 + [(2)(9.80m/s + [(2)(9.80m/s2 2 )(470m)])(470m)]

vvff22 = 9212 m2/s2

vf = 96.0 m/s

d = 0.470 km vi = 0 m/s vf = ? a = 9.80m/s2 t = ?

Example MExample M Determine the Determine the t

d = vviit + .5att + .5at22

d = 0 + .5at+ .5at22

d/.5a = td/.5a = t22

tt22 = 470m/[(.5)(9.80m/s 470m/[(.5)(9.80m/s22)) t = 9.79 s

d = 0.470 km vi = 0 m/s vf = 96.0 m/s a = 9.80m/s2 t = ?

Complete 9 and 10 on WS VComplete 9 and 10 on WS V9. To calculate the depth of a well a physics student 9. To calculate the depth of a well a physics student

drops a rock into the well. 4.5 seconds after the rock drops a rock into the well. 4.5 seconds after the rock is dropped the student sees it hit the bottom. The is dropped the student sees it hit the bottom. The rock accelerates downwards at 9.80 m/srock accelerates downwards at 9.80 m/s22..a. How deep is the well?a. How deep is the well?

b. How fast is the rock traveling the instant before it hits the b. How fast is the rock traveling the instant before it hits the bottom? bottom?

10. Flossy Fletcher was curling her hair when she 10. Flossy Fletcher was curling her hair when she dropped the curling iron. The curling iron fell 1.651m dropped the curling iron. The curling iron fell 1.651m to the floor.to the floor. a. How fast was the iron traveling when it hit the floor?a. How fast was the iron traveling when it hit the floor?

b. How long was it in the air?b. How long was it in the air?

Complete 9 and 10 on WS VComplete 9 and 10 on WS V5. To calculate the depth of a well a physics student drops 5. To calculate the depth of a well a physics student drops

a rock into the well. 4.5 seconds after the rock is a rock into the well. 4.5 seconds after the rock is dropped the student sees it hit the bottom. The rock dropped the student sees it hit the bottom. The rock accelerates downwards at 9.80 m/saccelerates downwards at 9.80 m/s22..a. How deep is the well? a. How deep is the well? 99.2m99.2m

b. How fast is the rock traveling the instant before it hits the b. How fast is the rock traveling the instant before it hits the bottom? bottom? 44.1 m/s44.1 m/s

6. Flossy Fletcher was curling her hair when she dropped 6. Flossy Fletcher was curling her hair when she dropped the curling iron. The curling iron fell 1.651m to the floor.the curling iron. The curling iron fell 1.651m to the floor. a. How fast was the iron traveling when it hit the floor? a. How fast was the iron traveling when it hit the floor? 5.69 m/s5.69 m/s

b. How long was it in the air? b. How long was it in the air? 0.581 s0.581 s

Example NExample N

A ball is shot upwards with a velocity of 114 A ball is shot upwards with a velocity of 114 m/s. m/s.

A.A. How high will it rise? How high will it rise?

B.B. How long will it take for the ball to How long will it take for the ball to return to the earth? return to the earth?

Determine your knowns first!!Determine your knowns first!!

Why is vWhy is vff 0 m/s? 0 m/s?

It stops and begins to fall.It stops and begins to fall.

d = ? vi = -114 m/s vf = 0m/s a = 9.80m/s2 t = ?

Example NExample N Determine the Determine the d

vvff22 = v = vii

22 + 2a + 2aΔΔd d

(v(vff22 - v - vii

22) /(2a) = d) /(2a) = d

d d =[(0m/s)=[(0m/s)2 2 - (-114m/s)- (-114m/s)22 ]/[(2)(9.80m/s ]/[(2)(9.80m/s22)])]

d = -663m ( upward displacement)d = -663m ( upward displacement)

d = ? vi = -114 m/s vf = 0 m/s a = 9.80m/s2 t = ?

Example NExample N Determine the Determine the t

vvff = v = vii + at + at

(v(vff – v – vii)/a = t)/a = t

t = (0 m/s - t = (0 m/s - --114m/s)/9.80m/s114m/s)/9.80m/s22

t = 11.6 st = 11.6 s

ARE YOU SURE?ARE YOU SURE?

What goes up must come down!!!!!What goes up must come down!!!!!

The question was how long it will take to return to earth.The question was how long it will take to return to earth.

This is only half the time!This is only half the time!

x =- 663 m vi = -114 m/s vf = 0 m/s a = 9.80m/s2 t = ?

Example NExample N Determine the Determine the t

Total time in the air = 2(11.6 s) = 23.2sTotal time in the air = 2(11.6 s) = 23.2s

d = -663 m vi = -114 m/s vf = a = 9.80m/s2 t = ?

Questions like this:

A ball is thrown straight up. At the top of its path its acceleration is?About 10 m/s2

9/21Today we will review motion graphs, then we will delve into advanced kinematic equations. (James Bond!)Have your “Moving Man” lab out as well as your Summary of graphs.I will not be here after school: Physics meeting.

DemoDemo

Dropping ball into moving boxDropping ball into moving box

10/510/5Open kinematic notes to Example OOpen kinematic notes to Example O

Remember moving man lab is due Remember moving man lab is due Monday. We will have a quiz Monday Monday. We will have a quiz Monday over graphing.over graphing.

6 week test make ups 6 week test make ups

Monday after school. Monday after school.

Last day!Last day!

Example O James Bond is standing on a bridge 15

meters above the river below. He needs to escape his pursuers. He sees a speed boat in the distance coming toward him. The boat is moving at constant velocity of 2.5 m/s. How far away should the boat be when 007 jumps off the bridge if he wants to land in the boat? Neglect air resistance.

Example OWhat do you know about 007? d = 15 m vi = 0

a = 9.8 m/s2

What do you know the boat? v = 2.5 m/sWhat do we want them to have incommon? Time!!!!What determines the time? 007 fall

Example ODetermine time with data from 007.What formula?

Δd = vΔd = viiΔΔt + ½at + ½aΔΔtt22

t = 1.75 secondsUse the time it takes 007 to fall to determine distance of boat when hejumps.What formula?

vvavgavg = Δd/ = Δd/ΔΔtt

d = 4.38 md = 4.38 m

Example P

A truck is traveling at 80km/h in aschool zone. A police car starts from rest just as the speeder passes it and accelerates at a constant rate of 3.24m/s2 . When does the police car catch the speeding truck? What

distance does the police car cover to catch the speeder?

Example PWhat do you know about the truck? v = 80km/h What do you know about the police? vi = 0 m/s

a = 3.24m/s2

What do we want them to have incommon?Distance from where the truck passed the police to where the police catchesup.

Example PWould you agree that this distanceoccurs in the same amount of time forboth vehicles?What formula can you use to determine distance about the truck?d = vtWhat formula can you use to determine distance about the police?

Δd = vΔd = viiΔΔt + ½at + ½aΔΔtt22

Set the two formulas equal to each other!

Example Pvt = vviiΔΔt + ½at + ½aΔΔtt22

If we substitute the values for the truckon the left and the police on the right,what are we solving for?TIME!!Truck: v = 80km/hPolice: vi = 0 m/s a = 3.24m/s2

What is the next step?Change 80km/h to m/s with DATruck: v = 22.2 m/s

Example PNow substitutevt = vviiΔΔt + ½at + ½aΔΔtt22

Truck: v = 22.2 m/sPolice: vi = 0 m/s a = 3.24m/s2

vviiΔΔt for police equals?t for police equals?

0(22.2 m/s)t = (.5)(3.24m/s2)t2 (22.2 m/s)t = (1.62m/s2)t2

22.2 m/s = (1.62m/s2)t t = 13.7 sec

Example Pt = 13.7 secNow we can solve for distance using information from truck or the police. It is the same! Which one would you do?I would choose the truck! Easier formula.d = vtd = (22.2 m/s)(13.7 s) = 304 mSummary: It will take 13.7 seconds for police to catch up over a distance of 304 m

9/20Goal: Self guided inquiry to determine the differences between position time graphs and velocity time graphs.Pick up Moving Man WS and Graph Summary SheetLog on to a laptop and go to my webpage via KCHS. You may have to share.

Wednesday we will discuss special problems such as 11 & 12 on Unit 03 WS VI. You should try to see if you can answer them. All of WS VI is due on Thursday except #3.Kinematics test on Friday.

Moving Man Inquiry LessonGoals:Plot data appropriately in a position time or velocity time graphWhat does the slope in a position time graph indicate?What does the slope in a velocity time graph indicate?Compare and contrast the following types of motion in a position time and velocity time graph:

No motionConstant motion (uniform velocity)Constant motion (uniform acceleration)

Understand how + and – is used to indicate direction

Open the following link and choose run now!

The Moving Man - Motion, Velocity, Acceleration – PhET

http://phet.colorado.edu/en/simulation/moving-man

Motion GraphingMotion GraphingDistance, Velocity, and Distance, Velocity, and

AccelerationAcceleration

Motion Graphing Reference

Wed 9/1Wed 9/1Pick up 3 pages at frontPick up 3 pages at front

Turn in WS II to the blue sorterTurn in WS II to the blue sorter

Turn in Yahtzee Graph to blue sorterTurn in Yahtzee Graph to blue sorter

Goal:Goal:– Apply understanding of graphing to D Apply understanding of graphing to D

vs T, V vs T, and A vs T Graphsvs T, V vs T, and A vs T Graphs

10/2Yesterday we did test corrections and made up tests and Meter Stick LabI will be not available today after schoolWednesday after school is last day for retakes. See me today if you plan on doing this.Please have grade slip signed and returned by Wednesday.Have HW VI out and ready to go overDownload Motion Graphs now. Print to one note

-500

-400

-300

-200

-100

0

100

200

300

400

500

0 10 20 30 40 50 60 70 80 90 100

dis

pla

cem

en

t (m

ete

rs)

time (seconds)

Displacement-Time Graph

Series1

d vs t graphd vs t graph

Slope of line is velocitySlope of line is velocity

Linear line represents a constant velocityLinear line represents a constant velocity

Horizontal line represents no motionHorizontal line represents no motion

Curved line represents accelerationCurved line represents acceleration

Steeper slope represents greater velocitySteeper slope represents greater velocity

Slope = Slope = d /d /t = velocityt = velocity

Distance from detector CAN be indicatedDistance from detector CAN be indicated

v vs t graphv vs t graphSlope of line is accelerationSlope of line is acceleration

Linear line represents uniform accelerationLinear line represents uniform acceleration

Horizontal line represents constant velocity, Horizontal line represents constant velocity, a=oa=o

Curved line represents changing accelerationCurved line represents changing acceleration

Steeper slope represents greater accelerationSteeper slope represents greater acceleration

Slope = Slope = v /v /t = accelerationt = acceleration

Distance from detector cannot be indicated, Distance from detector cannot be indicated, only direction: away is positive and towards only direction: away is positive and towards is negativeis negative

a vs t grapha vs t graph

Linear line– acceleration is Linear line– acceleration is changingchanging at at a constant ratea constant rateHorizontal line– uniform acceleration(the Horizontal line– uniform acceleration(the acceleration stays the same)acceleration stays the same)Curved line– acceleration is changing Curved line– acceleration is changing non-uniformlynon-uniformlySteeper slope-- greater change in aSteeper slope-- greater change in aSlope = Slope = a /a /tt

Obj 15: Comparing graphsObj 15: Comparing graphsNo motion (v=0)No motion (v=0)

velocity vs. time

00.20.40.60.8

1

1 2 3 4 5 6

time

ve

loc

ity

Series1

acceleration vs. time

00.20.40.60.8

1

1 2 3 4 5 6

time

ac

ce

lera

tio

n

Series1

Distance Vs. Time

0

2

4

6

1 2 3 4 5

time

dis

tan

ce

Series1

Constant Velocity (a=0) positive Constant Velocity (a=0) positive directiondirection

velocity Vs. Time

0

2

4

6

1 2 3 4 5

time

ve

loc

ity

Series1

Distance vs. time

0

10

20

30

1 2 3 4 5 6

time

dis

tan

ce

Series1

acceleration vs. time

00.20.40.60.8

1

1 2 3 4 5 6

time

ac

ce

lera

tio

n

Series1

Constant velocity (a=0) negative Constant velocity (a=0) negative directiondirection

acceleration vs. time

00.20.40.60.8

1

1 2 3 4 5 6

time

ac

ce

lera

tio

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velocity vs. time

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Begin Linear Motion CalculationsBegin Linear Motion Calculations

A young science student named A young science student named Earl N. Meyer walks 150 meters due Earl N. Meyer walks 150 meters due east and then turns around and east and then turns around and walks 30 meters due west.walks 30 meters due west.

What is the total What is the total distancedistance??

What is the What is the displacementdisplacement ? ?

Which is scalar?Which is scalar?

Which is a vector?Which is a vector?

A Tiger Belle walks straight south A Tiger Belle walks straight south for 12.6m then walks due east for for 12.6m then walks due east for 19.4m. 19.4m. What is the total What is the total distancedistance walked by walked by the Tiger Belle?the Tiger Belle?What is the Tiger Belle’s What is the Tiger Belle’s displacement?displacement?How to describe direction How to describe direction quantitatively?quantitatively?

A picture is worth a 1000 words..A picture is worth a 1000 words..Free Body DiagramsFree Body Diagrams

Arrows represent vectorsArrows represent vectorsLength of arrow corresponds to magnitude Length of arrow corresponds to magnitude of vectorof vectorConnect the tail of one vector to the arrow Connect the tail of one vector to the arrow tip of the othertip of the otherNo matter what route you take from point A No matter what route you take from point A to point B your final displacement vector will to point B your final displacement vector will be the samebe the sameThe final displacement vector is called the The final displacement vector is called the resultant vectorresultant vectorDraw in the resultant vector from the tail of Draw in the resultant vector from the tail of the first vector to the arrow head of the the first vector to the arrow head of the secondsecond

Free Body DiagramsFree Body Diagrams

Adding VectorsAdding Vectors

If two vectors are at If two vectors are at right angles to each right angles to each other the resultant other the resultant can be calculated can be calculated

with with

AA22 + B + B22 = C = C22

SOH CAH TOASOH CAH TOAThis is a good time to review This is a good time to review SOH CAH TOASOH CAH TOASine = opposite / hypotenuseSine = opposite / hypotenuseCosine = adjacent / hypotenuseCosine = adjacent / hypotenuseTangent = opposite / adjacentTangent = opposite / adjacentThese only work for right These only work for right triangles!triangles!

Remember…Remember…

S H

OC H

A

T A

O

SOH-CAH-TOA

Naming the sidesNaming the sides

A right angledtriangle

The angle weare interested in.

H

This is the longest side— the hypotenuse.

O

This side is oppositeour angle.

AThis side is adjacentto our angle.

Naming the sidesNaming the sides

H = Hypotenuse

O = Opposite

A = Adjacent

H

O

A

O

H

AH

OA

HO

A H

O

A

Remember…Remember…

S H

OC H

A

T A

O

SOH-CAH-TOA

What’s this What’s this SOHCAHTOA?SOHCAHTOA?

Ever wondered what the Ever wondered what the sinsin, , coscos and and tantan keys on your calculator are for? keys on your calculator are for?– ‘‘sin’sin’ == ‘sine’‘sine’– ‘‘cos’cos’ == ‘cosine’‘cosine’– ‘‘tan’tan’ == ‘tangent’‘tangent’

Sin, cos Sin, cos andand tan tan are the link between are the link between the angles and sides in a right angled the angles and sides in a right angled triangle.triangle.

SineSine

30°

4cm

8cmH =

O =

S HO

Here we know the Hypotenuse and the Opposite side.

So we use the SOH triangle.

This tells us that sin 30° = 4/8 = 0.5.

You can check with a calculator that sin 30° is 0.5.

What happens when you don’t know the angle?What happens when you don’t know the angle?

We can find the usable number mentioned previously using the ratios.

The problem is we know need to convert it back into the original angle.

The Buttons on your calculator are…

Sin Cos Tan

The opposite of these are SHIFT then

Sin-1 Cos-1 Tan-1

Work sample problems: solving Work sample problems: solving right trianglesright triangles

If two vectors are not at right If two vectors are not at right angles to each other then we angles to each other then we must use the Law of Cosines:must use the Law of Cosines:

CC22 = A = A22 + B + B22 – 2AB cos – 2AB cos ““” ” or Theta, is any unknown or Theta, is any unknown angle but in this case it is the angle but in this case it is the angle between the two vectorsangle between the two vectors

The SwimmerThe Swimmer

A swimmer attempts to swim due north to the pier 2.00 miles away but the current takes him at a bearing of 40°. After a while he notices he is due east of the pier. How far has he travelled?

Step 1. Draw a diagram.

pier

2.00

mile

s

40°?

The SwimmerThe Swimmer

?2 40°

Step 2. Identify the sides.

Here we have the Adjacent side and want to find the Hypotenuse. So we use the CAH triangle.

C H

A

Putting our finger on H shows that H = A/C

= 2.00 ÷ (cos 40°)= 2.00 ÷ 0.766= 2.61 miles

The Church SteepleThe Church Steeple

Eric decides to find the height of the steeple of his local church. He measures a distance of 50. m along the ground. The angle of elevation of the top of the steeple is 35°. How high is the steeple?

Step 1. Draw a diagram.

50.m 35°

?

The Church SteepleThe Church Steeple

?

50

35°

Step 2. Identify the sides.

Here we have the Adjacent side and want to find the Opposite. So, we use the TOA triangle.

Putting our finger on O shows that O = T × A

= (tan 35°) × 50.= 0.70 × 50.= 35 m

T AO

Finding An Angle (1)Finding An Angle (1)

At Heathwick airport there is a forest just 500. m from the end of the runway. The trees can be as tall as 30. m. What is the minimum angle of climb if aircraft are to avoid the trees?

Step 1. Draw a diagram.

30.m

500.m?

Finding An Angle (2)Finding An Angle (2)30

500

Step 2. Identify the sides

Here we have the Adjacent and Opposite sides and want to find an angle. So, we use the TOA triangle.

Putting our finger on T shows that… tan = O/A

= 30. ÷ 500.= 0.060

T AO

Now we can use the inverse tan to find the angle. = tan-1 0.060 = 3.4°

Remember…Remember…

S H

OC H

A

T A

O

SOH-CAH-TOA

30°

? cm

8 cmH =

O =

S HO

Sin Sin Finding the OppositeFinding the Opposite

SOH-CAH-TOA? ?

Opp = Sin × Hyp

= (Sin 30°) × 8

= 4 cm

27°

? km

12.3 km

H =

A =

C HA

Cos Cos Finding the AdjacentFinding the Adjacent

SOH-CAH-TOA? ?

Adj = Cos × Hyp

= (Cos 27°) × 12.3

= 0.891 × 12.3

= 11.0 km

53°

? cm

T AO

Tan Tan Finding the OppositeFinding the Opposite

O =

A =

16 cm

SOH-CAH-TOA? ?

Opp = Tan × Adj

= (Tan 53°) × 16

= 1.327 × 16

= 21 cm

36°

87 m

? mH =

O =

S HO

Sin Sin Finding the HypotenuseFinding the Hypotenuse

SOH-CAH-TOA??

Hyp = Opp Sin

= 87 (Sin 36°)

= 87 0.5878

= 150 m

0.80 cm

? cmH =

A =

C HA

Cos Cos Finding the HypotenuseFinding the Hypotenuse

60°SOH-CAH-TOA

? ?

Hyp = Adj Cos

= 0.80 (Cos 60.°)

= 0.80 0.50

= 1.6 cm

30°

3.1 cm T AO

Tan Tan Finding the AdjacentFinding the Adjacent

O =

A = ? cm

SOH-CAH-TOA? ?

Adj = Opp Tan

= 3.1 (Tan 30.°)

= 3.1 0.5773

= 5.4 cm

What happens when you don’t know the angle?What happens when you don’t know the angle?

We can find the usable number mentioned previously using the ratios.

The problem is we know need to convert it back into the original angle.

The Buttons on your calculator are…

Sin Cos Tan

The opposite of these are SHIFT then

Sin-1 Cos-1 Tan-1

3.0 km

7.0 kmH =

O =

S HO

Sin Sin Finding the AngleFinding the Angle

SOH-CAH-TOA? ??

Sin = Opp Hyp

Sin = 3.0 7.0

Sin = 0.4285

= Sin-1 (0.4285)

= 25°

12.1 cm

14.5cm

H =

A =

C HA

Cos Cos Finding the AngleFinding the Angle

SOH-CAH-TOA? ??

Cos = Adj Hyp

Cos = 12.1 14.5

Cos = 0.834

= Cos-1 (0.834)

= 33.4 °

67.0 cm T AO

Tan Tan Finding the AngleFinding the Angle

O =

A = 187 cm

SOH-CAH-TOA? ??

Tan = Opp Adj

Tan = 67.0 187

Tan = 0.358

= Tan-1 (0.358)

= 19.7°

Adding Vectors GraphicallyAdding Vectors GraphicallyMake a scale drawing (eg. Make a scale drawing (eg. 1cm = 1km)1cm = 1km)Connect the tail of one vector Connect the tail of one vector to the arrow tip of the otherto the arrow tip of the otherDraw in the resultant vector Draw in the resultant vector from the tail of the first from the tail of the first vector to the arrow head of vector to the arrow head of the second.the second.

Usually the Y axis points due north Usually the Y axis points due north and the X axis points due eastand the X axis points due eastWhen describing the angle When describing the angle determine direction of adjacent determine direction of adjacent side, then describe direction in side, then describe direction in relation to adjacent side.relation to adjacent side.Use a protractor to measure the Use a protractor to measure the number of degrees the resultant is number of degrees the resultant is from a cardinal direction. e.g. 4 from a cardinal direction. e.g. 4 degrees south of westdegrees south of west

Instantaneous Velocity or Instantaneous Velocity or vv

– – the rate of motion (speed) at any the rate of motion (speed) at any given moment ex. Radar gungiven moment ex. Radar gun

v= v= dd tt

Average Velocity=Average Velocity=vv

the change in position divided by the the change in position divided by the time interval ex. Average speed time interval ex. Average speed for a trip for a trip

v= v= ∆d∆d = = ddff –d –d00

∆ ∆t tt tff-t-t00

Units m/s

AccelerationAcceleration

A change in velocity in a unit of timeA change in velocity in a unit of time

a= a= ∆v∆v = = vvff –v –voo

∆ ∆t tt tff-t-too

Units m/s2

Acceleration due to gravity on Acceleration due to gravity on earthearth

– – this is a change in velocity caused this is a change in velocity caused by the force of attraction between by the force of attraction between the object and the earth. The the object and the earth. The acceleration due to gravity on earth acceleration due to gravity on earth is relatively constant everywhere on is relatively constant everywhere on earth although there are slight earth although there are slight variations due to the earth not being variations due to the earth not being perfectly round. perfectly round.

COPY THIS DOWN BEFORE COPY THIS DOWN BEFORE CLASS STARTSCLASS STARTS

Pick up WS I & get a calculatorPick up WS I & get a calculatorWe had a quiz yesterday on We had a quiz yesterday on

trianglestrianglesThe accepted value for the The accepted value for the acceleration due to gravity on earth acceleration due to gravity on earth are:are:

• • 9.80 m/sec/sec or 9.80 m/sec9.80 m/sec/sec or 9.80 m/sec22

Below is a ticker tape diagram. Below is a ticker tape diagram. What is the explanation for the What is the explanation for the

spacing of the dots?spacing of the dots?

start end

Great Website for Linear Motion

http://www.glenbrook.k12.il.us/gbssci/phys/class/1DKin/U1L1a.html

Homework: go to this website, click on Homework: go to this website, click on Lesson 2 and read Ticker Tape Lesson 2 and read Ticker Tape Diagrams. Answer the 2 questions at Diagrams. Answer the 2 questions at end of this section.end of this section.

Galileo’s Kinematics Lab Report

Purpose StatementConstruct your own data tables for Hypothesis A, B, and C. Make sure each table has a title and all columns are labeled. This requires a ruler!Graph for Hypothesis A, B, and C. Make sure each graph has a title and axes are labeled with magnitude and unit. This requires a ruler!Answer Questions for Hypothesis A, B, and C in complete sentences. To justify your answer means you reference the supporting data.

Galileo’s Kinematics Lab Report

Purpose StatementConstruct your own data tables for Hypothesis A, B, and C. Make sure each table has a title and all columns are labeled. This requires a ruler!Graph for Hypothesis A, B, and C. Make sure each graph has a title and axes are labeled with magnitude and unit. This requires a ruler!Answer Questions for Hypothesis A, B, and C in complete sentences. To justify your answer means you reference the supporting data.

Galileo’s Kinematics Lab Report

Purpose StatementConstruct your own data tables for Hypothesis A, B, and C. Make sure each table has a title and all columns are labeled. This requires a ruler!Graph for Hypothesis A, B, and C. Make sure each graph has a title and axes are labeled with magnitude and unit. This requires a ruler!Answer Questions for Hypothesis A, B, and C in complete sentences. To justify your answer means you reference the supporting data.

Galileo’s Kinematics Lab Report

Purpose StatementConstruct your own data tables for Hypothesis A, B, and C. Make sure each table has a title and all columns are labeled. This requires a ruler!Graph for Hypothesis A, B, and C. Make sure each graph has a title and axes are labeled with magnitude and unit. This requires a ruler!Answer Questions for Hypothesis A, B, and C in complete sentences. To justify your answer means you reference the supporting data.