Two Dimensional Kinematics
1.
A tennis ball falls off a cliff 10 meters above the ground with an initial horizontal speed of 5 meters per second
as shown above. The time between the object's leaving the roof and hitting the ground is most nearly
(A)
3 2
s
2
(B)
3
s
2
(C)
2 s
(D) 4 s
(E)
5 2s
2.
John and Bryan are on a boat that is capable of a maximum speed of 10 kilometers per hour in water, and wish
to cross a river 2 kilometer wide to a point directly across from their starting point. If the speed of the water in
the river is 5 kilometers per hour, how much time is required for the crossing?
(A) 0.05 hr (B) 0.1 hr
(C) 0.2 hr
(D) 1 hr (E) Cannot be found
3.
A projectile is fired from the surface of the Earth with a speed of 400 meters per second at an angle of 45°
above the horizontal. If the ground is level, what is the maximum height reached by the projectile?
(A) -16 m
4.
(C) 3520 m
(D) 4,000 m
(E) 6,000 m
A projectile is fired from the surface of the Earth with a speed of 150 meters per second at an angle of 60°
above the horizontal. If the ground is level, what is the maximum height reached by the projectile?
(A) 100 m
5.
(B) 1000 m
(B) 300 m
(C) 540 m
(D) 860 m
(E) 1000 m
A rock is dropped from the top of a 80-meter tower, and at the same time a ball is thrown from the top of the
tower in a horizontal direction. Air resistance is negligible. The ball and the rock hit the level ground a
distance of 40 meters apart. The horizontal velocity of the ball thrown was most nearly
(A) 5.7 m/s
(B) 10 m/s
(C) 14.1 m/s
(D) 20.2 m/s
(E) 28.3 m/s
6.
At a particular instant, a student is on the ground sees a box falling with speed v1 at an angle to the vertical.
To a pilot flying horizontally at constant speed relative to the ground, the box appears to be falling vertically
with a speed v2 at that instant. What is the speed of the pilot relative to the ground?
(A) v1 + v2
7.
(B) v1 - v2
(C) v2-v1
(D)
v1 v 2
2
2
(E) v 1  v 2
2
2
A physics intern has a spring-loaded gun that can fire a marble to a height h if fired straight up. The same gun
is pointed at an angle of 30° from the vertical, what is the maximum height the marble can reach?
(A) h/4
(B)
3h
2 2
(C) h/2
(D)
h
2
(E) h
Questions 8-9
A marble is shot and follows a parabolic path shown above. Air resistance is negligible. Point Y is the highest point
on the path.
8.
Which best indicates the direction of the velocity, if any, of the marble at point Y?
(A)
(B)
(C)
(D)
(E) There is no speed of the ball at point Y.
9.
Which of the following indicates the direction of the net force on the marble at point X?
(A)
(B)
(C)
(D)
(E)
10. A projectile is launched with an initial velocity with a horizontal component vhor and a vertical component vver.
Air resistance is negligible. When the projectile is at its highest, which of the following shows the vertical and
horizontal components of its velocity and the vertical component of its acceleration?
Velocity
Velocity
Acceleration
(A)
vver
vhor
0
(B)
vver
0
0
(C)
0
vhor
0
(D)
0
0
g
(E)
0
vhor
g
11. A target at point X lies flat on the ground 6 m from the side of a cliff that is 20 m tall, as shown above. A physics
student rolls a ball off the horizontal cliff in the direction of the target. Air resistance is negligible. The horizontal
speed with which the ball must leave the top of the cliff if it is to strike the target is most nearly
(A) 3/4 m/s
(B)
2 m/s
(C)
5
m/s
(D) 3 m/s
2
(E)
4
5
m/s
3
12. A physics student wants to hit a target with a rubber band ball from 11.3 meters away. If he throws the ball at a
speed of 15 m/s and the target is at the exact same height as where the ball is thrown, what angle from the
horizontal must he throw the ball to hit the target?
(A) 0
(B) 15°
(C) 30°
(D) 40°
(E) 45°
13. An airplane pilot is moving with a velocity v and drops a package. In the absence of air resistance where is the
package relative to the airplane at the moment it hits the ground?
(A) Behind the airplane (B) In front of the airplane
determined without knowing how height the plane is
distance traveled by the airplane.
(C) Directly below the airplane (D) Cannot be
(E) Cannot be determined without knowing the
14. At what angle must a student throw a ball in order to achieve its maximum distance?
(A) 0°
(B) 30°
(C) 45°
(D) 60°
(E) 90°
15. If a projectile is launched with an initial velocity vo at an angle Ѳ from the horizontal, which of the following
best represents the height the projectile achieve?
(A) vosin2Ѳ/g
(B) vo2sin2Ѳ/2g
(C) vocos2Ѳ/2g
(D) vo2cos2Ѳ/2g
(E) vocos2Ѳ/g
Question 16-18
The x- and y- coordinates of a particle in motion, as a function of time, are given:
x = 8t2 – 4t + 1
y = 2t3 – 3t2 + 6t – 3
16. The x- and y- components of the average velocity, in the interval from t = 0 s to t = 3 s are:
(A )vx = 36 m/s, vy = 42 m/s
(D)vx = -36 m/s , vy = -42 m/s
(B) vx = -20 m/s , vy = 15 m/s
(E)vx = 25 m/s , vy = 29 m/s
(C) vx = 20 m/s , vy = 15m/s
17. The x- and y- components of the instantaneous velocity at t= 2 s are:
(A) vx = -24 m/s, vy = 8 m/s
(D) vx = -36 m/s , vy = 42 m/s
(B) vx = 28 m/s , vy = 18 m/s
(E) vx = 12 m/s , vy = 8 m/s
(C) vx = 20 m/s , vy = 15m/s
18. The x- and y- components of the instantaneous acceleration at t=3 s are:
(A) ax = 16 m/s2, ay = 30 m/s2
(B) ax = 16 m/s2, ay = 0 m/s2
(D) ax = 16 m/s2, ay = 8 m/s2
(E) ax = 0 m/s2, ay = 30 m/s2
(C) ax = 0 m/s2, vy = 0 m/s2
19. Which of the following statements are true regarding projectile motion?
(A) (Vx)2 + (Vy)2 = constant.
(B) Acceleration is +g when the object is rising and –g when falling.
(C) In the absence of friction the trajectory will depend on the object’s mass as well as its initial velocity
and launch angle.
(D) The velocity of the object is zero at the point of maximum elevation
(E) The horizontal motion is independent of the vertical motion.
20. Two cannon balls are launched simultaneously off a cliff. The two cannon balls have different masses and
different initial velocities. Which will strike the ground first?
(A)The heaviest one
(B) The lightest one
(E) They will strike the plane at the same time
(C) The slowest one
(D) The fastest one
The x- and y- coordinates of a particle in motion, as a function of time, are given:
x = 5t2 – 5t + 6
y = 3t3 – 2t2 + 4t – 3
21. At the instant the x-component of velocity is equal to zero, the y-component of acceleration is:
(A) 5 m/s2
(B) 0.5 m/s2
(C) 2 m/s2
(D) –10 m/s2
(E) – 5 m/ s2
22. Which of the following pairs of angles will result in the same maximum horizontal range of a projectile?
(A)  = 45,  = 30
(D)  = 30,  = 60
(B)  = 60,  = 45
(E)  = 75,  = 25
(C)  = 90,  = 30
Question 23-24:
A projectile is fired at time t = 0 s, from the edge of a cliff, with initial velocity components of v ox = 50 m/s and voy =
400 m/s. The total time of the projectile is 200 s.
23. The magnitude of the velocity at time t= 20 s is:
(A) 204 m/s
(B) 190 m/s
(C) 210 m/s
(D) 319 m/s
(E) 400 m/s
(D) 7250 m
(E) 6780 m
24. The horizontal distance D is closest to:
(A) 10000 m
(B) 7000m
(C) 8000
25. The y-coordinate of the projectile when its x-coordinate is 4000 m is closest to:
(A) 1000 m
(B) 700 m
(C) 63360 m
(D) -550 m
(E) 640 m
The acceleration of a particle is given by the equation:
a(t) = 12t – 8
26. Given that vo = 0, at what time does the particle come to rest?
(A) 1/2 s
(B) 3/4 s
(C) 2/3 s
(D) 4/3 s
(E) 12 s
Questions 27 – 28
A projectile is launched with an initial velocity vo at an angle Ѳ from the horizontal.
27. How long does it take the projectile, if it reaches a maximum height h, to hit the ground?
(A) vo2sin2Ѳ/g
(B) vo2cos2Ѳ/g
(C)
2h / g
(D) 2vosinѲ/g
(E)vo2cosѲ/2g
28 The maximum distance traveled by the object is about:
(A) vo2sin2Ѳ/g
(B) vo2sin2Ѳ/g
(C) vo2cosѲ/2g
(D) vo
2h / g
(E) vo2cos2Ѳ/g
Questions 29-30
An soccer ball is launched horizontally off a cliff that is 12 meters tall with in initial velocity of 5 meters per second.
The ball experiences a resistant force where the ball decelerates by ax=3 m/s2 in the x direction and ay=3.8 m/s2 in
the y direction.
29. How long does the object fall for?
(A) 1 s
(B) 2 s
(C) 3 s
(D) 4 s
(E) 5 s
(C) 4 m
(D) 11 m
(E) 18 m
30. How far does the object travel?
(A) 0 m
(B) 2 m
Question 31-37
As shown above an object is launched with an initial velocity of 10 meters per second at an angle of 53°. It travels
in a parabolic path and lands on a cliff that is 10 meters tall.
31. What are the vertical and horizontal components of the ball’s velocity at the beginning of its flight?
(A) vx = 6 m/s, vy = 8 m/s
(D) vx = 8 m/s , vy = 6 m/s
(B) vx = 5 m/s , vy = 5 m/s
(E) vx = 0 m/s , vy = 10 m/s
(C) vx = 10 m/s , vy = 10 m/s
32. What are the vertical and horizontal components of the ball’s velocity at the apex of its flight?
(A) vx = 6 m/s, vy = 8 m/s
(D) vx = 8 m/s , vy = 6 m/s
(B) vx = 6 m/s , vy = 0 m/s
(E) vx = 8 m/s , vy = 0 m/s
(C) vx = 0 m/s , vy = 0 m/s
33. What is the acceleration vector at the start of its flight?
(A)
(B)
(C)
(D)
(E)
34. What is the velocity vector at the apex of its flight?
(A)
(B)
(C)
(D)
(E)
35. How fast is the ball traveling at its apex?
(A) 10 m/s
(B) 8 m/s
(C) 6 m/s
(D) 2 m/s
(E) 0 m/s
36. What is the velocity vector just before it lands?
(A)
(B)
(C)
(D)
(E)
37. What is the acceleration vector just before it lands?
(A)
(B)
(C)
(D)
(E)
Question 38-39:
38. Using the graph above, find the position of the particle at t = 10 s:
(A) 10 m
(B) 25 m
(C) 30 m (D) 35 m
(E) 40 m
39. Using the same graph, determine the instantaneous acceleration at t = 8 s:
(A) 2 m/s2
(B) 4 m/s2
(C) ½ m/s2 (D) 1 m/s2
(E) 3 m/s2
40. The x- and y- components of a particle’s acceleration is given as a function of time, are
ax = -4t + 1
ay = 2t + 3
What is the magnitude of the particle’s velocity at t= 1s if initial velocity is equal to zero?
(A) 4.12 m/s
(B) 2.1 m/s
(C) 5.3 m/s
(D) -2.1 m/s (E) – 5 m/s
Answers:
Question Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Answer
C
C
D
D
B
D
A
A
D
E
D
B
C
C
B
C
B
A
E
E
A
D
C
A
E
D
D
B
B
C
A
B
D
B
C
C
D
C
C
A