MOM – C – Elastic Collisions – Sample Problems
1. Abbey and Mia are in the basement playing pool. On Abbey's recent shot, the cue ball was moving east at 82
cm/s when it struck the slower 5-ball moving in the same direction at 24 cm/s. The 5-ball immediately
speeds up to 52 cm/s. Determine the post-collision speed of the cue ball.
2.
A 0.112-kg billiard ball moving at 154 cm/s strikes a second billiard ball of the same mass moving in
the opposite direction at 46 cm/s. The second billiard ball rebounds and travels at 72 cm/s after the
head-on collision. Determine the post-collision velocity of the first billiard ball.
3.
A 225-kg bumper car (and its occupant) is moving north at 98 cm/s when it hits a 198-kg car
(occupant mass included) moving north at 28 cm/s. The 198-kg car is moving north at 71 cm/s after
the head-on collision. Determine the post-collision velocity of the 225-kg car.
4.
A 4.88-kg bowling ball moving east at 2.41 m/s strikes a stationary 0.95-kg bowling pin.
Immediately after the head-on collision, the pin is moving east at 5.19 m/s. Determine the postcollision velocity of the bowling ball.
2. A 0.112-kg billiard ball moving at 154 cm/s strikes a second billiard ball of the same mass moving in
the opposite direction at 46 cm/s. The second billiard ball rebounds and travels at 72 cm/s after the
head-on collision. Determine the post-collision velocity of the first billiard ball.
(0.112 kg)•(154 cm/s) + (0.112 kg)•(-46 cm/s) = (0.112 kg)•v + (0.112 kg)•(72 cm/s)
17.248 kg•cm/s + -5.152 kg•cm/s = (0.112 kg)•v + 8.064 kg•cm/s
4.032 kg•cm/s = (0.112 kg)•v
v = 36 cm/s
3.
A 225-kg bumper car (and its occupant) is moving north at 98 cm/s when it hits a 198-kg car
(occupant mass included) moving north at 28 cm/s. The 198-kg car is moving north at 71 cm/s after
the head-on collision. Determine the post-collision velocity of the 225-kg car.
(225 kg)•(98 cm/s) + (198 kg)•(28 cm/s) = (225 kg)•v + (198 kg)•(71 cm/s)
22050 kg•cm/s + 5544 kg•cm/s = (225 kg)•v + 14058 kg•cm/s
13536 kg•cm/s = (225 kg)•v
v = 60. cm/s (60.16 cm/s)
4.
A 4.88-kg bowling ball moving east at 2.41 m/s strikes a stationary 0.95-kg bowling pin.
Immediately after the head-on collision, the pin is moving east at 5.19 m/s. Determine the postcollision velocity of the bowling ball.
(4.88 kg)•(2.41 m/s) = (4.88 kg)•v + (0.95 kg)•(5.19 m/s)
11.76 … kg•m/s = (4.88 kg)•v + 4.93 … kg•m/s
6.83 … kg•m/s = (4.88 kg)•v
v = 1.40 m/s