Question

a ball is going 20m/s after a train but it when the ball was at rest. How fast was the train going before it hit the ball

Answer 1

Consider the situation:

A ball of mass m is moving at 20m/s attached to a train after the collision with a train of mass M. Initially the ball was at rest. How fast was the train going before it hit the ball?

Solution

According to momentum conservation:

$$Mu+m·0=(M+m)v,\\\space\\ u=\frac{(M+m)v}{M}=20\frac{M+m}{m}.$$