Ch3 – Metric Conversions. “King Henry David Usually drinks chocolate milk” Giga.. Mega.. Kilo...

Ch3 – Metric Conversions

Ch3 – Metric Conversions

“King Henry David Usually drinks chocolate milk”

Giga . . Mega . . Kilo Hecta Deka Basic deci centi milli . . micro . . nano . . pico Units


Giga . . Mega . . Kilo Hecta Deka Basic deci centi milli . . micro . . nano . . pico Units

(Meters) (Liters)

(Grams) G . . M . . K H D U d c m . . μ . . n . . p


Giga . . Mega . . Kilo Hecta Deka Basic deci centi milli . . micro . . nano . . pico Units G . . M . . K H D U d c m . . μ . . n . . p

Exs: 505 grams = __________ kilograms

90 cm = __________ m

2.05 L = __________ mL

75 km = __________ m

75 nm = __________ m

700 μm = __________ m

Describing Motion

Describing MotionVectors –

Scalars –

Describing MotionVectors – describe things that have both magnitude and direction

Use arrows to represent them.Scalars –


Use arrows to represent them.Scalars – have only magnitude



Examples:1. Speed (v) – vs.2. Velocity ( ) – v



Examples:1. Speed (v) – how fast something is going vs.2. Velocity ( ) – v



Examples:1. Speed (v) – how fast something is going vs.2. Velocity ( ) – how fast its going in a particular directionv



Examples:1. Speed (v) – how fast something is going vs.2. Velocity ( ) – how fast its going in a particular direction

1. Distance (d) – vs.2. Displacement ( ) –

v

d




1. Distance (d) – how far something moves vs.2. Displacement ( ) –

v

d




1. Distance (d) – how far something moves vs.2. Displacement ( ) – how far something moves in a particular

direction. (Straight line distance)

v

d

Displacement = velocity . timed = v . t


Measure velocity in: miles per hour (mph)

Kilometers per hour (km/hr)Meters per second (m/s)


Measure velocity in: miles per hour (mph)

Kilometers per hour (km/hr)Meters per second (m/s)

Ex: A car passes a sign that reads 40.1 km while traveling east thru a straight valley. 30 minutes later it passes a sign that reads 84.5 km. How fast was the car traveling? (Use m/s)

Ch3 HW#1 1-3 + metric conversions

Ch3 HW#11. A desert tortoise covers 1.5 m in 45 sec. What is its speed?

2. A bicyclist travels 55 km in 1 hr 30 mins. Speed?

3. Car passes sign that reads 25.6 km traveling north. 1 hr 15 min later it passes a sign that reads 115.2 km. Speed?

Metric Conv1. 7 mm = _____ cm 5. 6.3 cm = _____ m 9. 7.2 μ = _____ cm2. 8.1 mm = _____ m 6. 3.3 cm = _____ km 10. 1.2 km = _____ nm3. 8.2 mm = _____ km 7. 3.6 m = _____ km 11. 1.7 km = _____

cm4. 7.5 cm = _____ mm 8. 5.2 pm = _____ mm


(d=vt)

2. A bicyclist travels 55 km in 1 hr 30 mins. Speed?55 km = 55,000 m1.5 hr 3600 sec

1 hr3. Car passes sign that reads 25.6 km traveling north. 1 hr 15 min later it passes a sign that reads 115.2 km. Speed?

d = 115.2 – 25.6 = 89.6 km = 89,600 m 1.25 hr 3600 sec

1 hr

smm

t

dv /073.0

sec45

5.1

= 5400 sec

= 4500 sec


(d=vt)



d = 115.2 – 25.6 = 89.6 km = 89,600 m 1.25 hr 3600 sec

1 hr

smm

t

dv /073.0

sec45

5.1

smm

t

dv /2.10

sec5400

000,55

= 5400 sec

= 4500 sec


(d=vt)



d = 115.2 – 25.6 = 89.6 km = 89,600 m 1.25 hr 3600 sec

1 hr

smm

t

dv /073.0

sec45

5.1

smm

t

dv /2.10

sec5400

000,55

= 5400 sec

= 4500 sec

smm

t

dv /9.19

sec4500

600,89

Ch3 HW#1Metric Conv G . . M . . KHDUdcm . . μ . . n . . p1. 7 mm = ____ cm2. 8.1 mm = ______ m3. 8.2 mm = ________ km4. 7.5 cm = ___mm

5. 6.3 cm = _______ m6. 3.3 cm = ________ km7. 3.6 m = _______km8. 5.2 pm = ____________mm

9. 7.2 μm = _______ cm10. 1.2 km = ______________nm11. 1.7 km = ______ cm

Ch3 HW#1Metric Conv G . . M . . KHDUdcm . . μ . . n . . p1. 7 mm = 0.07 cm2. 8.1 mm = 0.0081 m3. 8.2 mm = 0.0000082 km4. 7.5 cm = 75 mm

5. 6.3 cm = _______ m6. 3.3 cm = ________ km7. 3.6 m = _______km8. 5.2 pm = ____________mm

9. 7.2 μm = _______ cm10. 1.2 km = ______________nm11. 1.7 km = ______ cm


5. 6.3 cm = 0.063 m6. 3.3 cm = 0.000033 km7. 3.6 m = 0.0036 km8. 5.2 pm = 0.000 000 0052 mm

9. 7.2 μm = _______ cm10. 1.2 km = ______________nm11. 1.7 km = ______ cm


5. 6.3 cm = 0.063 m6. 3.3 cm = 0.000033 km7. 3.6 m = 0.0036 km8. 5.2 pm = 0.000 000 0052 mm

9. 7.2 μm = 0.00072 cm10. 1.2 km = 12,000,000,000,000 nm11. 1.7 km = 170,000 cm

Ch3.3 Velocity and Acceleration

Velocity – speed in a specific direction



Average velocity – since speed can vary in most cases, use average speed.

- easiest method is finding total distance divided by total time





t

dv





Instantaneous velocity – speed and direction at that moment(GPS and speedometer in your car)

t

dv





Instantaneous velocity – speed and direction at that moment(GPS and speedometer in your car)

Ex1) Standing on a roof 100m above the ground, a kid drops a water balloon 4.5s it hits the ground. What was the average speed?

t

dv

Ex2) Hair grows at an average rate of 3x10-9 m/s. Find the length after one year.

Ex2) Hair grows at an average rate of 3x10-9 m/s. Find the length after one year.

d = v.t

= (3x10-9m/s)(3.2x107s)

= 0.09m (9 cm)

What if the hair was already 10cm long before the year started, how long would it be a year later?

To find distance when not starting at zero:

df = di + v.t

Ex3) A car passes a sign that reads 213.8km. If the cruise control is setat 88km/hr, what does a sign read ½ hour later?

Acceleration – a measure of the change in velocity

speeding up: a = (+) slowing down: a = (–)

Ex4) Set up only: A driver traveling at 25m/s slows at a constant rate of 8.5m/s2. What is the total distance the car moves before stopping?

Ch3 HW#2 4 – 8

t

va

Lab3.1 – Motion

- due tomorrow

- go over Ch3 HW#2 @ beginning of period

Ch3 HW#2 4 – 8 (Set up, no solve, except 8)4. A dragster starting from rest accelerates at 49 m/s2.

How fast is it going when it has traveled 325m?

5. The same dragster reaches the end of the drag strip rolling at 100km/hr,when it opens its parachute. It rolls to a stop in 150m.How much time does it take to come to a stop?

6. A ball is thrown upward at 25m/s. Gravity slows it at 10m/s2.What height does it reach?

7. A ball is hit and then slowly comes to a stop in 5 sec.Draw. When is it going fastest? What is its final speed? Is its accl +/-?

8. Solve: Enter a toll road at 1pm. After traveling 55km, the ticket is stamped 2:30pm. What was the average speed.At any time could it have been going faster than the average?Why speed not velocity?

Ch 4 - Vectors-Have magnitude (length) and point in a direction

Ch 4 - Vectors-Have magnitude (length) and point in a direction

Ex1) Draw vectors representing velocities: 15 m/s North

10 m/s East

Vectors can be added together, called vector addition


- Graphically, place them head to tail



- Mathematically, vector addition means 3 possibilities:



- Mathematically, vector addition means 3 possibilities:

1. Point same direction: Add

2. Point opposite directions: Subtract

3. Point perpendicular: Pythag

Ex2) Vector Addition: a) 2 km east and 1 km east

b) 3 km east and 2 km west

c) 3 km north and 4 km east

Ex2) Vector Addition: a) 2 km east and 1 km east

(Red is the resultant vector)

b) 3 km east and 2 km west


c) 3 km north and 4 km east


--The order you add vectors doesn’t matter

2km 1km

2 + 1 = 3 km

3km

1km 2km3 – 2 = 1

3km

4km

5 km

km543 22

HW#2) A shopper walks from the door of the mall to her car 250 m down a lane of cars, then turns 90° to the right and walks an additional 60

m. What is the magnitude of the displacement of her car from the mall

door?

HW#2) A shopper walks from the door of the mall to her car 250 m down a lane of cars, then turns 90° to the right and walks an additional 60

m. What is the magnitude of the displacement of her car from the mall

door?

Mall

60

250d = √2502+602

= 257m

3. A boat is rowed South at 3 m/s down a river that flows South at 5 m/s. What speed does an observer from shore see the boat

moving?

-A boat is rowed North at 3 m/s up a river that flows South at 5 m/s. What speed does an observer from shore see the boat

moving?

-A boat is rowed East at 3 m/s across a river that flows South at 5 m/s. What speed does an observer from shore see the boat

moving?


moving?


moving?


moving?

3m/s

5m/a

8m/s


moving?


moving?


moving?

3m/s

5m/a

8m/s

35

2m/s


moving?


moving?


moving?

3m/s

5m/a

8m/s

35

2m/s

Θ

3

5v = √ 32 +52

v = 5.8m/s

HW#8. An airplane flies due north at 150 km/h with respect to the air. There is a wind blowing at 75 km/h to the east relative to the ground. What is the plane’s speed with respect to the ground?

Ch4 HW#1 1 – 8

HW#8. An airplane flies due north at 150 km/h with respect to the air. There is a wind blowing at 75 km/h to the east relative to the ground. What is the plane’s speed with respect to the ground?

v = √ 1502 + 752 = 167.7 km/hr

75 km/hr

150 km/hr

Ch4 HW#1 1 – 8

Lab3.2 More Motion

- due tomorrow (in school terms)

- Ch4 HW#1 due at the beginning of the period

Ch4 HW #1 1 – 8

1. A car is driven 125 km due west, then 65km due south. What is the magnitude of its displacement?

2. (In class)

Ch4 HW #1 1 – 8

1. A car is driven 125 km due west, then 65km due south. What is the magnitude of its displacement?

2. (In class)

125 km

65 km d = √1252 + 652

= 141 km

3. In class

4. A car moving east at 45 km/hr for 1 hour turns and travels north at 30 km/hr for 2 hours. What are the magnitude of its displacement?

5. You are riding in a bus moving slowly through heavy traffic at 2.0 m/s. You hurry to the front of the bus at 4.0 m/s relative to the

bus. What is your speed relative to the street?

3. In class

4. A car moving east at 45 km/hr for 1 hour turns and travels north at 30 km/hr for 2 hours. What are the magnitude of its displacement?

5. You are riding in a bus moving slowly through heavy traffic at 2.0 m/s. You hurry to the front of the bus at 4.0 m/s relative to the bus. What is your speed relative to the street?

d = v ∙ t = (30km/hr)(2hr)= 60km

45 km

60 kmd = √452 + 602

2 4 d = 2 + 4 = 6 m/s

6. A motorboat heads due east at 11 m/s relative to the water across a river that flows due north at 5.0 m/s. What is the velocity of the motorboat with respect to the shore?

7. A person walks 3 blocks north, turns and walks 2 blocks east, turns and walks 4 more blocks north, and finally turns east and walks 2 more blocks east. In terms of city blocks, how far is the person from where they started? (Hint: vectors can be added in any order. Maybe you can switch the order so that they make a triangle to pythag.)

8. In class

11m/s5m/s

6. A motorboat heads due east at 11 m/s relative to the water across a river that flows due north at 5.0 m/s. What is the velocity of the motorboat with respect to the shore?

7. A person walks 3 blocks north, turns and walks 2 blocks east, turns and walks 4 more blocks north, and finally turns east and walks 2 more blocks east. In terms of city blocks, how far is the person from where they started? (Hint: vectors can be added in any order. Maybe you can switch the order so that they make a triangle to pythag.)

8. In class

11m/s5m/s

7 block N

4 blocks E

Trigonometry & Vector Components

SOHCAHTOA


SOHCAHTOA

in

pp

yp

os

dj

yp

an

pp

dj


SOHCAHTOA

in

pp

yp

os

dj

yp

an

pp

dj

sinΘ =

cosΘ =

tanΘ =

opphyp

adjhyp

oppadj


SOHCAHTOA

in

pp

yp

os

dj

yp

an

pp

dj

sinΘ =

cosΘ =

tanΘ =

opphyp

adjhyp

oppadj

Θhypotenuse

adjacent

opposite

Θ

A

cosΘ = adjhyp

cosΘ = Ax

A

Ax = A∙ cosΘ

sinΘ = opphyp

sinΘ = Ay

A

Ay = A∙ sinΘ

tanΘ = oppadj

tanΘ = Ay

Ax

Θ = tan-1 ( )Ay

Ax

Θ

Ay

Ax

Ay

A

Ax2 + Ay

2 = A2

cosΘ = adjhyp

cosΘ = Ax

A

Ax = A∙ cosΘ

sinΘ = opphyp

sinΘ = Ay

A

Ay = A∙ sinΘ

tanΘ = oppadj

tanΘ = Ay

Ax

Θ = tan-1 ( )Ay

Ax

Ex 1) A bus travels 23 km on a straight road that is 30° north of east. What are the north and east components if its displacement?

Ex 2) A boat travels with a speed of 20 m/s due east. The current moves at 5 m/s due south. What is the speed if the boat w.r.t. the shore, and what angle does it head?

Ex 1) A bus travels 23 km on a straight road that is 30° north if east. What are the north and east components if its displacement?


dy

dx

dy30°23 km

dx = d ∙ cosΘ = (23km) ∙ cos30° =19.9km

dy = d ∙ sinΘ = (23km) ∙ sin30° =11.5km

Ex 1) A bus travels 23 km on a straight road that is 300 north if east. What are the north and east components if its displacement?


v =?

20 m/s

5 m/sΘ

v2 = 202 + 52

= 20.6 m/s

Θ = tan-1( ) = 14° 520

dy

dx

dy30°23 km

dx = d ∙ cosΘ = (23km) ∙ cos30° =19.9km

dy = d ∙ sinΘ = (23km) ∙ sin30° =11.5km

HW #9. What are the components of a vector of magnitude 1.5 m at an angle of 35° from the positive x-axis?

HW #9. What are the components of a vector of magnitude 1.5 m at an angle of 35° from the positive x-axis?

dy

dx

dy350d = 1.5m

dx = d ∙ cosΘ = 1.5m ∙ cos350 = 1.2m

dy = d ∙ sinΘ = 1.5m ∙ sin350 = .86m

Ch 4 HW #2 9-15

For lab 4.1:

- due tomorrow

- Ch4 HW#2 due at beginning of perioddy

dx

Θ

}

Ch4 HW#2 9 – 15 10. A hiker walks 14.7 km at an angle 35° south of east.

Find the east and north components of this walk.

11. An airplane flies at 65 m/s in the direction 149° counterclockwise from east. What are the east and south components of the plane’s velocity?

Ch4 HW#2 9 – 15 10. A hiker walks 14.7 km at an angle 35° south of east.

Find the east and north components of this walk.

11. An airplane flies at 65 m/s in the direction 149° counterclockwise from east. What are the east and south components of the plane’s velocity?

dy

dx

dy

35°14.7 km

dx = d ∙ cosΘ = (14.7km) ∙ cos35° =

dy = d ∙ sinΘ = (14.7km) ∙ sin35° =

vy

vx

149°

65m/s

vx = v ∙ cosΘ = (65m/s) ∙ cos149° =

vy = v ∙ sinΘ = (65m/s) ∙ sin149° =

12.A golf ball, hit from the tee, travels 325 m in a direction 25° south of east. What are the east and north components of its displacement?

13.An airplane flies due south at 175 km/h with respect to the air. Wind blowing at 85 km/hr to the east wrt the ground. Plane’s speed wrt the ground?

12.A golf ball, hit from the tee, travels 325 m in a direction 25° south of east. What are the east and north components of its displacement?

13.An airplane flies due south at 175 km/h wrt the air. Wind blowing at 85 km/hrto the east wrt the ground. Plane’s speed wrt the ground?

dy

dx

dy

25°325m

dx = d ∙ cosΘ = (325m) ∙ cos25° =

dy = d ∙ sinΘ = (325m) ∙ sin25° =

v =?175km/hr

85km/hr

Θ

v2 = 1752 + 852

= 194.6 km/hr

Θ = tan-1( ) = 26°85175

14.A rowboat is paddled at 5 m/s, with respect to the water, perpendicular to the shore of a river that flows at 4 m/s with respect to the shore. What is the velocity (both magnitude and direction) of the boat wrt the

shore?

15. An airplane has a speed of 285 km/h with respect to the air. There is a side wind blowing at 65 km/h with respect to Earth. What is the plane’s speed and direction with respect to the ground?

Θ5

4


shore?


Θ5

4v = √ 42 +52

v = 6.4 m/s

Θ = tan-1( ) = 38.7°4 5

vplane

vwind

Θv = ?


shore?


Θ5

4v = √ 42 +52

v = 6.4 m/s

Θ = tan-1( ) = 38.7°4 5

vplane

vwind

Θv = ?

v = √ 2852 +652

v = 292 km/hr

Θ = tan-1( ) = 12.8°65 285

Ch3,4 Practice Problems20. Solve: A jet flies from LA to NY, a distance of 6000km in 5.5hrs.

What is its average speed?

21. Solve: A bike travels at a constant speed of 4m/s for 5 sec.How far does it go?

22. Set up a model: A bike accelerates from 0.0m/s to 4.0m/s in 4 sec.What distance does it travel?

23. Set up a model: A student drops a ball from a window 3.5m abovethe sidewalk. The ball accelerates at 9.8m/s2. How fast is it goingright as it hits the sidewalk?

24. Set up: you throw a ball downward from a window at a speed of 2.0m/s. (HW) The ball accelerates at 9.8m/s2. How fast is it going right before

it hits the ground 2.5m below?

25. You row your boat perpendicular to shore of a river that flows at 10m/s. Your boat has a velocity of 4m/s wrt the water.What is the velocity of the boat wrt the shore? At what angle does it cross?

26. An airplane is traveling at 700km/hr north wrt the air, into a headwind (HW) blowing at 75km/hr south wrt the ground. What is the plane’s speed

wrt the ground?

27. The Mars Lander has a vertical velocity of 5.5m/s towards the surface (HW) of Mars. It also has a horizontal velocity of 3.5m/s due to Martian

wind. At what speed and angle does it descend?

28. The space shuttle is rising with an average velocity of 100m/s as it is (HW) being pushed East by upper atmospheric wind of 25m/s.

What speed and direction do viewers on ground see?

29. Hiker leaves camp, walks 4km East, then 6 km South, then 3km East, then 5km North, then 10km West, and then 8km North.How far is he directly from camp?

Ch3,4 Review Problems30. Set up model: A car is traveling at 30m/s when the driver sees a chicken

crossing the road. He takes 0.8 sec to react, then steps on the brakesand slows to a stop at 7.0m/s2. What is total distance traveled?

31. Solve: A car passes a mileage marker reading 155.5km. It travels 2.5hrs before passing another marker. If the car had an average speed of 88km/hr, what will the sign read?

32. You walk 30m south then 30m east. Find the magnitude and direction of the resulting displacement.

33. A balloon rises at 15m/s, wind is blowing at 6.5m/s West. What is velocity and direction balloon moves wrt the ground?

34. A small plane is coasting to earth at 100mph at 20° below the horizontal.At what rate is it approaching the ground?

35. Find the x and y components of a 20km displacement vector at 60°.

(The end)

100 90 80 70vel 60 (m/s) 50 40 30 20 10 1 2 3 4 5 6 7 8 9 10

time (sec)

Ch3 – Metric Conversions. “King Henry David Usually drinks chocolate milk” Giga.. Mega.. Kilo...

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