Name:__________________________Physics Chapter 3 Study GuideUseful Information:

a2+b2=c2 sin θ=opphyp

cosθ= adjhyp

tanθ= oppadj

sin Aa

=sin Bb

= sinCc

c2=a2+b2−2 ab cosC a=v f−vit

x=(v f+vi2 )t x=vi t+12a t 2 v f

2=vi2+2a x

A Basic Understanding:•Chapter 3 Odd Numbered Core Problems•Chapter 3 Review Problems: 7, 11, 21, 27, 28, 29, 30, 32, 34, 42, 44, 48, 56.•Complete Trigonometry

Pushing to be Better:•Chapter 3 Your Try Problems•Chapter 3 Even Numbered Core Problems•Chapter 3 Review Problems: 1, 2, 4, 5, 6, 8, 12, 22, 23, 25, 31, 33, 35, 37, 43, 45, 46, 47, 49, 50, 53, 54, 61.•Standardized Test Prep 1-12.•Complete Law of Sines, Law of Cosines•Complete Projectile Motion

Digging Deeper:•Chapter 3 Review Problems: 16, 18, 26, 36, 55, 57, 59.•Individual Inquiry

Note on Equations: Remember that Pythagorean Theorem and Tangent, Sine and Cosine only apply to right triangles. Law of Sines and Law of Cosines apply to ANY triangle.

For projectile motion, you just use the same equations from Chapter 2. You just do it twice: once for horizontal, once for vertical. Remember that the horizontal acceleration is al-ways 0 m/s2 and the vertical acceleration is always -9.81 m/s2. Remember that the time is the same for both parts. And, remember that the distances, initial velocities and final velocities do not have to be the same for both parts.

Physics Ch. 3 Study Guide page 1 of 1

Name:_____________________________Chapter 3 Worked Examples Physics1) A snowball is thrown from the soccer field at somebody who is walking the path to Willoughby. The horizontal distance from the thrower to the path is 50 m. The vertical distance from the field to the path is 8.0 m. The snowball is throw at an initial angle of 25° above hori-zontal. What speed is the snowball thrown at?

Your try: The thrower from the worked example throws a snowball at the same speed, but changes the angle to 45° above horizontal. What is the new horizontal distance that the snow-ball with travel? (Assume the vertical drop is the same.)

Physics Ch. 3 Worked Examples page 1 of 2

2) A small airplane can cruise at 75 m/s. The Warren, VT and Morrisville Airports are located at the following coordinates: Warren Airport: UTM 18 673847E 4887087NMorrisville Airport: UTM 18 689553E 4934296N. During the flight, there is a 15 m/s wind blow-ing at 90°.a) What is the displacement between the Warren and Morrisville Airports?b) What heading should you give the plane to fly on a straight line between the two airports?c) How much time (neglecting take-off and landing) does it take to fly between the two air-ports?

Your try: A small airplane can cruise at 81 m/s. The Rutland, VT and Barre Airports are located at the following coordinates: Rutland Airport: UTM 18 663605E 4830625N Barre Airport: UTM 18 699609E 4896788N. During the flight, there is a 19 m/s wind blowing at 190°.a) What is the displacement between the Rutland and Barre Airports?b) What heading should you give the plane to fly on a straight line between the two airports?c) How much time (neglecting take-off and landing) does it take to fly between the two air-ports?

Physics Ch. 3 Worked Examples page 2 of 2

Physics Chapter 3 Your Try Problems (Based on various worked examples.)

3) Video 3c: The two short sides of a right triangle are 5cm and 9cm long. Find a) the length of the hypotenuseb) the angle opposite the 5cm long side.

4) Video 3d: A 12’ long board is leaning up against a wall at an angle of 60° above the horizon-tal. a) How far up the wall is the top of the board?b) How far is the bottom of the board from the wall?

5) Videos 3j-p: A home run lands in the bullpen, a horizontal distance of 105m from home plate. The hang time is 5.3 seconds. Calculate the initial velocity of the ball when it left the bat. (Ignore air resistance. There is no vertical distance between home plate and the bullpen.)

6) ADVANCED!! Videos 3j-p: A fairway is inclined at a steady 10° above horizontal. A golf ball is hit up the fairway with an initial velocity of 45 m/s at 35° above the horizontal. Calculate the distance along the fairway from where the ball is struck to where it lands. (Ignore air resis-tance.)

7) Videos 3q-s: An ocean current is flowing from south to north at 3 knots. Your boat can travel through the water at 8 knots. You wish to follow a bearing of 270° (due west). a) What should you heading be?b) How fast are you moving along your bearing?

8) Videos 3e,f,g,u,v: From campus, West Burke has a displacement of 8.22 km at 313°, and Lyn-donville has a displacement of 10.14 km at 230°. Calculate the displacement of West Burke if you are in Lyndonville.

9) ADVANCED!! Videos 3e,f,g,u,v: The UTM coordinates of the Kitchel Science Center are: 19T 0269491E 4941886N. The elevation is 408m. a) Find the elevation of the summit of Burke Mountain in meters.b) Find the UTM coordinates of the summit of Burke Mountain.c) Find the 2D displacement from the science center to the summit. (Distance and direction.)d) Find the 3D distance from the science center to the summit. (Hint: a2+b2+c2=d2 )e) Find the angle of elevation from the science center to the summit.f) Express the displacement as a radius, inclination and azimuth. (Hint, you’ve calculated all these already, you just need to learn the vocab.)

Answers to Chapter 3 Your Try Problems Worked Example 1: A small airplane can cruise at 81 m/s...a) 75.3 km at 28.6°b) 24.3°c) 1200 seconds = 20.0 minutes

Worked Example 2: The thrower from the worked example throws...new horizontal distance = 55.3 m

3) Videos 3c: The two short sides of a right triangle are...a) 10.3 cmb) 29°

4) Video 3d: A 12’ long board is leaning up against a wall...a) 10.4’ up the wall.b) 6’ from the wall.

5) Videos 3j-p: A home run lands in the bullpen...initial velocity = 32.7 m/s at 52.7° above horizontal

6) ADVANCED!! Videos 3j-p: A fairway is inclined at a steady 10°...distance along fairway = 147 meters.

7) Videos 3q-s: An ocean current is flowing from...a) Bearing = 248°b) Speed along bearing = 7.4 knots.

8) Videos 3e,f,g,u,v: From From campus, West Burke has a displacement of...Displacement of West Burke from Lyndonville: 12.25 km at 8°.

9) ADVANCED!! Videos 3e,f,g,u,v: The UTM coordinates from a point on...a) 996.7mb) 19T 0270277 4939349c) 2633 m at 156.4°d) 2704 me) 13.2°f) (2704 m, 13.2°, 156.4°)

Name:__________________________Physics Chapter 3 Core Problems1) Vector A has a magnitude of 30 units. Vector B is perpendicular to vector A and has a magnitude of 40 units. What would the magnitude of the resultant vector A + B be?A. 10 unitsB. 50 unitsC. 70 unitsD. zeroE. depends on the angle.

2) Choose the statement which is FALSE.A. An acceleration is a change in velocity.B. Average speed is distance traveled divided by elapsed time.C. Acceleration is a scalar.D. 50 meters per second is an example of a speed.E. A vector is a scalar with a direction.

3) A ball with a mass of 35 g is rolled along a counter top with a speed of 1.20m/s. At the exact instant that it reaches the edge of the counter, a 1.00 kg mass is rolled off the edge of the counter with a horizontal speed of 0.010 m/s. The height of the counter is 95.0cm. What is the time difference between when the ball and the mass hit the floor?

4) On the following triangle, find side c and angle A.

Physics Ch. 3 Core Problems page 1 of 2

4

3c

A 70°

5) On the following triangle, find side c and angle A.

6) A tennis ball is thrown off of a balcony at an angle of 30° above horizontal with an initial speed of 12 m/s. The balcony is 3.1 m above a parking lot. How far from the base of the balcony will the tennis ball land?

Physics Ch. 3 Core Problems page 2 of 2

2

1c

A

Name:_____________________________Trigonometry Physics

1) a) Use Pythagorean Theorem to find a.b) Use Sine to find B.

2) a) Use Tangent to find b.b) Use Cosine to find c.

3) Use any method to find:a) Ab) Bc) Cd) De) ef) a

Physics Trigonometry page 1 of 1

7.3

Ba

4.0

bc

54°2.8

a

e

a

A

BC

D

4.03.2

Name:_____________________________Law of Sines, Law of Cosines Physics1) Write the Law of Sines.

2) Write the Law of Cosines.

Use the Law of Sines and Cosines to find all sides and angles of the following triangles.

3)

4)

5)

Physics LOS/LOC page 1 of 1

6.4

79°

42°

5.2

4.4137°

30°

7.23.8

Name:_________________________Projectile Motion on a tilted table Physics

Setup:

•Put two identical books under the legs of a long table so that one long-side is higher than the other long side.•Place a "launch" tube on one of the higher corners of the table. The tube should be parallel to the longedge of the table.

Important: •For the beginning parts of this investigation, please just consider the motion of the ball when it is visible. That is, when it is on the table and not in the tube.•Mark where the end of the tube meets the table so that you can keep your placement consistent.

Part 1: Observing, Predicting, Data Collection

1) Raise a bit the end of the tube that's off the table. Put a ball bearing in the tube. Let it roll. Observewhat happens. Record your observations.

2) Predict what will happen to the motion of the ball if you raise or lower the end of the tube. Write out your predictions.

3) Put the ball bearing in the higher or lower tube. Observe what happens. Record whether your observations match your predictions.

4) What's causing the change in the behavior?

Phys Projectile Motion on tilted table page 1 of 3

Table

BookBook

“launch” tube

5) Now to get a bit more qualitative. Find the height of the tube that allows the ball to still cross the lower edge of the table. Find two equally sized spacers that you can place under the tube so that your height is reproducible. Place one spacer under the tube. Place the ball in the tube and measure what happens. Notice that we have gone from "observing" to "measuring." What do you need to measure? How do you measure it?

6) Write your prediction for what will happen when you add the second spacer so that the end of the tube is twice as high off the table.

7) Add the second spacer and launch the ball. Measure the outcome. Record your results.

8) Did your observations match your predictions? If so, why? If not, why not?

9) Now that you're gaining experience with the setup, are there any other predictions you could make? Repeat the cycle of prediction and observation until you feel that you've got things pretty well dialed in.

10) List all of the quantities that you can measure with the usual equipment that we use in Physics class.

11) Repeat the experiment with one spacer under the tube. Record all of the quantities you mentioned in step 9.

12) Repeat with two spacers under the tube.

Part 2: Mathematical Modeling

12) You now have a lot of numbers. We've been studying a lot of equations that are mathematical models that can be applied to this situation. Find as many valid relationships between your measured values as you can. Make sure that you quantify and attempt to explain any discrepancies and errors that you find.

13) Mathematical models also allow us to predict things that are hard to measure directly. If we are now comfortable that our measurements and models are valid, what hard to measure quantities can we calculate based off of our data? List them and calculate values for them.

14) In our experiment, some quantities stay the same whether there is one spacer under the tube or two. List the quantities that stay the same. Explain why they stay the same.

15) Other quantities change whether there is one spacer under the tube or two. List the quantities that change. Explain how the change. Explain why they change.

Phys Projectile Motion on tilted table page 2 of 3

Part 3: Extensions

16) We've been using the same steel ball bearing the whole time. Predict how the experiment would be effected if you used a steel ball bearing with a different diameter. Record your prediction.

17) Repeat the experiment with a different size ball bearing.

18) Predict what would happen if the ball was not made out of steel. What are some other possibilitiesfor a material? Record your prediction.

19) Repeat the experiment with different ball materials.

20) Our tube has always been parallel to the top edge of the table. What would happen if the tube was angled towards or away from the top edge of the table? (Hint, at this point we will most likely need to move the tube away from the top corner so that everything stays on the table.) Record your predictions, do the experiment.

Phys Projectile Motion on tilted table page 3 of 3