Question

A 1 kg billiard ball collides head on with a 0.1 kg marble that sits at rest on the table. The marble moves at 3 m/s in the same direction the billiard ball was originally moving. The billiard ball continues after the collision at 0.3 m/s. What was the initial speed of the billiard ball?

Answer 1

Let v be the billiard ball's initial speed. The total momentum of the ball-marble system is conserved between the times before and after their collision, so that

(1 kg) v + (0.1 kg) (0 m/s) = (1 kg) (0.3 m/s) + (0.1 kg) (3 m/s)

Solve for v :

v + 0 = 0.3 m/s + 0.3 m/s

v = 0.6 m/s