Question

A ball has a mass of 0. 25 kg and is moving to the right at 1. 0 m/s. It hits a ball of mass 0. 15 kg that is initially at rest. After the collision, the 0. 15 kg ball moves off to the right with a velocity of 0. 75 m/s. What is the final velocity of the 0. 25 kg ball? 0. 42 m/s to the right 0. 42 m/s to the left 0. 55 m/s to the right 0. 55 m/s to the left.

Answer 1

The ball that starts in motion has a momentum of

(0.25 kg) (1.0 m/s) = 0.25 kg•m/s

Note that we take "to the right" to be the positive direction.

The ball that starts at rest has zero momentum.

The total momentum of the system before collision is then

0.25 kg•m/s + 0 = 0.25 kg•m/s

After the collision, the first ball continues moving to the right but has slowed down. Its final momentum is

(0.25 kg) (0.75 m/s) = 0.1875 kg•m/s

Let v be the velocity of the other ball after they collide. Then its momentum after collision would be

(0.15 kg) v

Momentum is conserved throughout the collision, so that

0.25 kg•m/s = 0.1875 kg•m/s + (0.15 kg) v

Solve for v :

0.0625 kg•m/s = (0.15 kg) v

v ≈ 0.42 m/s

Since v has positive sign, the second ball moves at 0.42 m/s to the right.