Homework – Problem Solving with Collisions
1.
During a routine space mission, an astronaut falls through space at a rate of 200 m/s.
Determine the astronaut’s weight if he has a momentum of 1.6 104 kg  m/s .

1.6 104 kg  m/s
 80 kg
v
200 m/s
W  mg  (80 kg)(9.8 m/s 2 )  784 N
  mv  m 
2.

A baseball with a mass of 0.15 kg is thrown by a pitcher at a speed of 45 m/s and then hit
by a batter. The ball is in contact with the bat for 0.01 seconds and is driven directly into
center field with a speed of 55 m/s. What is the momentum of the thrown ball, the batted
ball, and the impulse on the ball.
  m  v  (0.15 kg)(45 m/s )  6.75 kg  m/s  or right
  m  v  (0.15 kg)(55 m/s )  8.25 kg  m/s  8.25 kg  m/s  or left
J  F  t     f  o  (8.25 kg  m/s )  (6.75 kg  m/s )  15 N  s
OR
J  F  t  mv  (0.15 kg)(55 m/s  45 m/s )  15 N  s
3.
An apple with a mass of 0.1 kg falls on Isaac Newton’s head from a height of 2 meters.
With what momentum does the apple hit Newton?
v 2f  vo2  2 gy  v f  2(9.8 m/s 2 )(2 m)  6.26 m/s  or down  6.26 m/s
  m  v  (0.1 kg)(6.26 m/s )  0.63 kg  m/s  0.63 kg  m/s  or down
4.
A rifle with a mass of 2 kg is used to fire a bullet of mass 0.05 kg. The bullet leaves the
gun with a speed of 200 m/s. What is the recoil velocity of the gun?
Explosion, 1  2, one-dimensional.
mt vo  mAvA  mBvB  0  (2 kg)(vA )  (0.05 kg)(200 m/s )  (2 kg)(vA )  (10 kg  m/s ) 
 10 kg  m/s  (2 kg)(vA )  vA  5 m/s  5 m/s  or left
Homework – Problem Solving with Collisions (cont.)
5.
A Cadillac with a mass of 2500 kg collides with a Volkswagen with a mass 1000 kg. Their
bumpers lock. The Cadillac is moving at a speed of 23.6 m/s at the time of impact and the
Volkswagen is standing still. Determine the speed and direction of the crash.
Inelastic collision, 2  1, one-dimensional.
mAvA  mBvB  mt v f  (2500 kg)(23.6 m/s )  (1500 kg)(0 m/s )  (3500 kg)(v f ) 
59000 kg  m/s  (3500 kg)(v f )  v f  16.86 m/s  16.86 m/s  or right
6.
Suppose that in the previous problem the Volkswagen was moving at a speed of 33.3 m/s
and the Cadillac at a speed of 4.2 m/s. They collide head-on and lock bumpers. Determine
the speed and direction of the crash.
Inelastic collision, 2  1, one-dimensional.
mAvA  mBvB  mt v f  (2500 kg)(4.2 m/s )  (1000 kg)(33.3 m/s )  (3500 kg)(v f ) 
(10500 kg  m/s )  (33300 kg  m/s )  (3500 kg)(v f ) 
(22800 kg  m/s )  (3500 kg)(v f )  v f  6.51 m/s  6.51 m/s  or left
Homework – Problem Solving with Collisions (cont.)
7.
A 350 kg car is moving 16 m/s north and collides with a 650 kg truck going 11 m/s east. If
they lock bumpers, how fast and in what direction will they be going after the collision?
Inelastic collision, 2  1, two-dimensional.
mAvA  mB vB  mt v f  (650 kg)(11 m/s E)  (350 kg)(16 m/s N)  (1000 kg)(v f ) 
(7150 kg  m/s E)  (5600 kg  m/s N)  (1000 kg)(v f ) 
(9081.99 kg  m/s @ 38.1)  (1000 kg)(v f )  v f  9.08 m/[email protected]