Question

A less massive moving object has an elastic collision with a more massive object that is not moving. Compare the initial velocity of the less massive object to it's final velocity

Answer 1

Assume that the small-massed particle is
`m` and the heavier mass particle is
`M`.

Now, by momentum conservation and energy conservation:

`mv = mv_(m) + Mv_(M)`

`mv^(2) = mv^(2)_(m) + Mv^(2)_(M)`

Now, there are 2 solutions but, one of them is useless to this question's main point so I excluded that point. Ask me in the comments if you want the excluded solution too.

`v_(m) = v(m - M)/(m + M)\\\\\\v_(M) = v(m + M)/(m + M)\\`

So now, we see that
`v_(m) < 0` and
`v_(M) > 0`. So therefore, the smaller mass recoils out.

Hope this helps you!

Bye!