Name: ___________________________
Date: ______________
Physics I H
Mr. Tiesler
Solutions to Momentum Homework Problems 16-20
16.) A ball of mass 0.440 kg moving east (  x direction) with a speed of 3.30 m/s collides headon with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and
direction of each ball after the collision?
Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. We have vA  3.30 m s and
vA  vB    vA  vB   vB  vA  vA
Substitute this relationship into the momentum conservation equation for the collision.
mA vA  mB vB  mA vA  mBvB  mA vA  mA vA  mB  vA  vA  
0.220 kg
 mA  mB 
vA 
 3.30 m s   1.10 m s  east 
0.660 kg
 mA  mB 
vB  vA  vA  3.30 m s  1.10 m s  4.40 m s  east 
vA 
17.) Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If one ball’s
initial speed was 2.00 m/s and the other’s was 3.00 m/s in the opposite direction, what will be
their speeds after the collision?
Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction. Let B represent
the ball moving at 3.00 m/s in the opposite direction. So vA  2.00 m s and vB  3.00 m s .
vA  vB    vA  vB   vB  5.00 m s  vA
Substitute this relationship into the momentum conservation equation for the collision, noting that
mA  mB .
mA vA  mB vB  mA vA  mB vB  vA  vB  vA  vB 
1.00 m s  vA   vA  5.00 m s   2vA  6.00 m s  vA  3.00 m s
vB  5.00 m s  vA  2.00 m s
The two balls have exchanged velocities. This will always be true for 1-D elastic collisions of
objects of equal mass.
18.) An archer shoots an arrow toward a 3.00x102 g target that is sliding in her direction at a
speed of 2.50 m/s on a smooth, slippery surface. The 22.5 g arrow is shot with a speed of 35.0
m/s and passes through the target, which is stopped by the impact. What is the speed of the
arrow after passing through the target?
19.) A 0.060 kg tennis ball, moving with a speed of 250 m/s, collides head-on with a 0.090 kg
ball initially moving away from it at a speed of 1.15 m/s. Assuming a perfectly elastic collision,
what are the speed and direction of each ball after the collision?
Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball. The initial direction of the
balls is the positive direction. We have vA  2.50 m s and vB  1.15 m s . Use Eq. 7-7 to obtain a
relationship between the velocities.
vA  vB    vA  vB   vB  1.35 m s  vA
Substitute this relationship into the momentum conservation equation for the collision.
mA vA  mB vB  mA vA  mBvB  mA vA  mBvB  mA vA  mB 1.35 m s  vA  
vA 
mA vA  mB  vB  1.35 m s 
mA  mB

 0.060 kg  2.50 m s    0.090 kg 1.15 m s  1.35 m s 
0.150 kg
 0.88 m s
vB  1.35 m s  vA  2.23 m s
Both balls move in the direction of the tennis ball’s initial motion.
20.) A rifle with a weight of 30.0 N fires a 5.0 g bullet with a speed of 3.00x102 m/s. (a) Find
the recoil speed of the rifle. (b) If a 700.0 N man holds the rifle firmly against his shoulder, find
the recoil speed of the man and his rifle.