Here are some useful equations:

S F = ma A = (A_x , A_y) B = (B_x ,B_y) A + B = (A_x+ B_x , A_y+ B_y) A - B = (A_x- B_x , A_y- B_y)
w = mg g = 9.8 m/s² You can take g = 10 m/s²
v =(v_x,v_y)=(v_0x + a_x t, v_0y + a_y t) x - x₀ = v_0x t + ½ a_x t² 2a_x (x - x₀ ) = v_x ² - v_0x²
x - x₀ = ½ (v_x + v_0x)t
position = (x , y) = (x₀ + v_0xt +  , y₀ + v_0yt +  ) velocity = (v_x , v_y ) = (v_ox+ a_xt , v_oy+ a_yt )
projectile motion:
a = ( 0, -g ) v = (v_x , v_y ) = (v_ox , v_oy-gt ) (x , y) = (x₀ + v_0xt, y₀ + v_0yt -  )
d = 

F_k = m _k N F_smax = m _s N
Conservation of momentum S (m_iv_i)_before = S (m’_iv’_i)_after (v is a vector)
Impulse = change of momentum S FD t = D (mv)
1.
A projectile is fired horizontally from a flare gun located 45.0 m above the ground. The projectile's speed as it leaves the gun is 250 m/s. The projectile remains in the air
A) 25 s   B) 20 s    C) 15 s    D) 5.5 s     E) 3 s
 
 

2)   A projectile is fired horizontally from a flare gun located above the ground. The projectile's speed as it leaves the gun is 250 m/s. The projectile remains 15 seconds in the air. The speed of the projectile as it strikes the ground is
A) 400 m/s    B) 345 m/s     C) 290 m/s     D) 250 m/s     E) 235 m/s

3) 
A medieval army is attacking a castle with very tall walls, 100 meters high. The army's (only) cannon is entrenched exactly 50 meters from the castle. The cannon fires balls at 80 m/s. The Head Knight decides that the cannon fires at an angle of 30 degrees above horizontal. After firing the ball:
A) falls down before wall          B) hits the wall at the height of 26 m     C) hits the wall at the height of 36 m
D) hits the wall at the height of 51 m         E) goes over the wall

4 ) Two pool balls collide on a pool table. Before the collision, ball A slides leftward at 2 m/s, and ball B is motionless. After the "head-on" collision, ball A slides leftward at 0.5 m/s. Both balls have mass m = 0.1 kg. The speed of ball B after the collision is:
A) 2 m/s leftward      B) 1.5 m/s leftward      C) 1 m/s leftward      D) 0.5 m/s leftward      E) 1 m/s rightward

5) Two pool balls collide on a pool table. Before the collision, ball A slides leftward at 5 m/s, and ball B is motionless. After the "head-on" collision, ball A slides leftward at 1 m/s and ball B slides leftward at 4 m/s. Both balls have mass m = 0.5 kg. The kinetic energy the system of two balls lost in this collision is
A)    2 J             B)4 J                C) 6 J                D)  8 J               E) 17 J

6) Block X, of mass 2 kg, is moving to the right at 8 m/s. Block Y, of mass 4 kg, is moving to the left at 12 m/s. The two blocks collide head-on. The ratio of the magnitude of the impulse exerted by X on Y to that exerted by Y on X is:
A) 1/4                    B) 1/3                 C) 1/2                      D)                       E) 1
7) A baseball of mass m moves with speed v and is hit by a bat so that the ball leaves the bat with speed V (V > v in opposite direction). The bat is in contact with the ball for time T. The average force (magnitude) of the bat on the ball during the time T is
A) m v / T           B) m V / T             C) m (V + v) / T              D) m (V - v) / T           E)   m (v²+V²) / (v + V)

8) A 4-kg body moving with speed 5m/s breaks up into two 1-kg and 3-kg pieces. The 1-kg body moves off at a right angle to the original 4-kg body trajectory with an unknown speed, as shown. The 3-kg body moves off at an angle of 48⁰ below the x - axis, as shown. The final speed of the 3-kg body is
A) 10 m/s           B)          C)             D)  3/4 v             E)  1/3 v

9) Two bodies, A and B, have equal kinetic energies. The mass of A is nine times that of B. The ratio of the momentum of A to that of B is:
A) 1/9                          B) 1/3                        C) 1                    D) 3                     E) 9

10) A 0.20 kg rubber ball is dropped from the window of a building. It strikes the sidewalk below at 30 m/s and rebounds at 20 m/s. The change in momentum of the ball as a result of the collision with the sidewalk is (in kg ×m/s):
A) 10.0                    B) 6.0                  C) 4.0                 D) 2.0                     E) (-6, +4)

II.

A block slides frictionlessly towards a ramp with speed v=15 m/s. While moving up the ramp, the block decelerates, and the magnitude of the deceleration is |a|=5 m/s². At the end of the ramp the block shoots into the air. Eventually the block lands on a plateau which is level with the top of the ramp. The ramp is L=12.5 meters long and makes a q = 30⁰ angle with the floor.

a) Find the speed of the block when it leaves the ramp. Ans. _________________

b) Find the components of the velocity vector at the top of the ramp. Ans. _____________________

c) Find the time to reach the maximum height. Ans. _____________________

d) Find the maximum height above the floor. Ans. _____________________

e) Find the time the block spent in the air. Ans. _____________________

f) Find the horizontal distance D the block made while in the air. Ans. _____________________

7. Find the velocity (components) of the block the moment just before hitting the plateau.

h) Find the speed of the block the moment just before hitting the plateau. Ans. ________________

III

A satellite, initially at rest, shoots two cannon balls A and B. The mass of the satellite without the cannon balls is 58 kg. Both balls move perpendicular to each other after the ejection. The linear momentum of A is 12 kg m/s and that of B is 5 kg m/s.

A) Draw a clear picture that illustrates the event. Don’t forget to draw a coordinate axis.

B) Find the magnitude of the linear momentum of the satellite after the ejection. Ans. ______________

C) Find the angle between the satellite’s momentum and the momentum of cannon ball A.

Ans. ________________

4. Find the kinetic energy of the system if the mass of A is 2 kg and the mass of B is 3 kg.

1E) 3 s
2 C) 290 m/s
3 B) hits the wall at the height of 26 m
4 B) 1.5 m/s leftward
5 A) 2 J
6 E) 1
7 C) m (V + v) / T
8 A) 10 m/s
9 D) 3
10 A) 10.0