Name: ________Answer Key _________ Date: ____________________________ Regents Physics Test #5 Review

Projectiles

1. Equations to know: (1) Ay = Asinθ (2) Ax = Acosθ

(3) v

a=t

f

f i

v vt t

Δ −=

Δ −i (4)

2f

avgv vv i+

= (5) d=vit+½at2

(6) vf=vi+at (7) vf2=vi2+2ad

2. Terms to know:

vector, magnitude, direction, resultant, component, trajectory, projectile

3. Read Chapter 7.

4. A ball is launched horizontally off a building. At the same time, a ball is dropped off the building. For the two balls, compare:

o the time taken to reach the ground Both hit at the same time o initial velocities in the x and y directions Vi in y direction = 0 for both, in x = 0 for

dropped ball. Launched ball Vi = some value. o the acceleration a = -9.81 m/s2 for both balls o the displacements in the x and y directions. dy is same for both, dx = 0 for dropped,

dx = some value for launched.

5. A soccer ball is kicked with an initial velocity of 15 m/s at an angle of 300 above the horizontal. Describe what happens to the vertical and horizontal components of its velocity as the football flies through the air and lands. Vertical velocity decreases until it hits top of path and then increases as heads back down. Horizontal velocity remains the same (no horizontal acceleration)

Directions: Read each question carefully and record your answers in the space provided. Be sure to show all work! Answers should be in significant figures. You will be graded on proper use of the GUESS method. These will be the same directions on the test. Practice the GUESS method now. 6. A stone is thrown horizontally at a speed of 5.0 m/s from the top of a cliff 78.4 m high.

a) How long does it take the stone to reach the bottom of the cliff?

2

2 2(78.4 )4.00

9.81 ms

d mt sa

= = =

b) How far from the base of the cliff does the stone strike the ground?

5.0 (4.00 ) 20.msx xd v t s m= = =

c) What are the horizontal and vertical components of the velocity of the stone just before it strikes the ground?

2( 9.81 )(4.00 ) 39.2 / down

5.0 / forward

mfy iy s

fx

v v at s m sv m s

= + = − =

=

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7. A player kicks a football from ground level at 27 m/s at an angle of 350 above the horizontal. Calculate the following.

a) the x and y components of the initial velocity.

sin 27 (sin35 ) 15 / up

cos 27 (cos 35 ) 22 / forward

msiy i

msix i

v v m sv v m s

θθ

= = ° =

= = ° =

b) the total time the ball is in the air.

2

15 /1.5

9.81

2( ) 2(1.5 ) 3.0

f itop m

s

total top

v v m st sa

t t s s

− −= = =

−

= = =

c) the distance the ball travels (horizontally) before it hits the ground.

22 (3.0 ) 66m

sx x totald v t s m= = =

d) its maximum height.

22 21 1

2 2(15 )(1.5 ) ( 9.81 )(1.5 ) 11m msy iy top top s

d v t at s s m= + = + − = 8. A ball is rolled down a ramp and projected horizontally from a height of 1.7 meters. It lands 2.6

meters away. Calculate its initial speed. [Note: This is similar to the Shoot for Your Grade Lab]

Step 1 – Solve for time using the height 2

2 2(1.7 )0.589

9.81y

ms

d mt sg

= = =

Step 2 – Use the time and x distance to solve for vx

2.64.4 /

0.589x

ixd mv m st s

= = =

9. The ball from question 8 is now raised to a height of 2.4 meters. Where is it going to land? [Hint:

The initial velocity does not change with a height change.]

Step 1 – Solve for new time using the new height 2

2 2(2.4 )0.699

9.81y

ms

d mt sg

= = =

Step 2 – Use the new time and vx from #8 to solve for dx

4.4 (0.699 ) 3.1m

sxd v t s m= = =

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Base your answers to questions 10 – 13 on the following information. A rock is launched at a speed of 10. m/s at an angle of 60.0 with the horizontal. It returns to the earth at the same level at which it was launched. 10. The shape of the path that the rock took was:

(A) straight line (B) circular (C) parabolic (D) hyperbolic

11. The initial vertical velocity of the rock is:

(A) 5.0 m/s (B) 8.7 m/s (C) 10. m/s (D) 20. m/s

12. The initial horizontal velocity of the rock is:

(A) 5.0 m/ s (B) 8.7 m/s (C) 10. m/s (D) 20. m/s

13. Which statement is true about the trajectory of the rock?

(A) It accelerates in both the vertical and horizontal direction (B) It accelerates in the vertical direction and travels at a constant velocity in the horizontal

direction. (C) It accelerates in the horizontal direction and travels at a constant velocity in the vertical

direction (D) It travels at a constant velocity in both the horizontal and vertical direction

Questions 14 and 15 refer to the following: Projectile A is launched horizontally at a speed of 20. meters per second from the top of a cliff and strikes a level surface below, 3.0 seconds later. Projectile B is launched horizontally from the same location at a speed of 30. meters per second. 14. How much time does it take projectile B to reach the level surface?

(A) 10. s (B) 4.5 s (C) 3.0 s (D) 2.0 s 15. Approximately how high is the cliff?

(A) 29 m (B) 44 m (C) 60. m (D) 104 m 16. A ball is thrown at an angle of 380 to the horizontal. What happens to the magnitude of the

ball’s vertical acceleration during the total time interval that the ball is in the air?

(A) It increases, then decreases. (B) It decreases, then increases. (C) It decreases, then remains the same (D) It remains the same

17. A football player kicks a ball with an initial velocity of 25 meters per second at an angle of 530

above the horizontal. What is the vertical component of the initial of the initial velocity of the ball?

(A) 20. m/s (B) 25 m/s (C) 15 m/s (D) 10. m/s

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Questions 18 through 20 refer to the following: A ball is thrown horizontally with an initial velocity of 20.0 meters per second from the top of a tower 60.0 meters high, as shown in the diagram below.

18. What is the horizontal velocity of the ball just before it reaches the ground?

(A) 20. m/s (B) 9.81 m/s (C) 34.3 m/s (D) 68.6 m/s 19. What is the approximate total time required for the ball to reach the ground?

(A) 2.04 s (B) 3.00 s (C) 3.50 s (D) 12.2 s 20. What is the initial vertical velocity of the ball?

(A) 60.0 m/s (B) 20.0 m/s (C) 9.81 m/s (D) 0 m/s 21. The diagram below shows a student throwing a baseball horizontally at 25 meters per second

from a cliff 45 meters above level ground.

Approximately how far from the base of the cliff does the ball hit the ground? [Neglect air resistance]

(A) 45 m (B) 75 m (C) 140 m (D) 230 m 22. A book is pushed with an initial horizontal velocity of 5.0 meters per second off the top of a

desk. What is the initial vertical velocity of the book?

(A) 5.0 m/s (B) 10 m/s (C) 2.5 m/s (D) 0 m/s

80

23. Which graph best represents the motion of an object whose speed is increasing?

24. A projectile is launched with an initial velocity of 200 meters per second at an angle of 300

above the horizontal. What is the magnitude of the vertical component of the projectile’s initial velocity?

(A) 200 sin30ms × ° (C) 200 cos 30m

s × °

(B) 200 /sin30

m s°

(D)200 /cos 30

m s°

Question 25 and 26 refer to the following: A golf ball leaves a golf club with an initial velocity of 40.0 meters per second at an angle of 40.0 with the horizontal.

25. What is the vertical component of the golf ball’s initial velocity?

(A) 25.7 m/s (B) 40.0 m/s (C) 30.6 m/s (D) 61.3 m/s 26. What is the total horizontal distance traveled by the golf ball during the first 2.50 seconds of flight?

(A) 40.0 m (B) 64.3 m (C) 76.6 m (D) 100. m

Answers:

6. a. 4

.00 s

b. 20. m

c. v

x = 5

.0 m

/s v

y = --3

9.2

m/s

7. a. v

x = 2

2 m

/s V

y = 15

m/s

b. 3.0

s c. 6

6 m

d. 11

m

8. 4.4

m/s

9. 3.1

m

10

. C 1

1. B

1

2. A

13

. B

14

. C 1

5. B

1

6. D

1

7. A

18

. A 1

9. C

20

. D

21

. B

22

. D

23

. A 2

4. A

25

. A 2

6. C

81

82