Assume that the small-massed particle is [tex]m[/tex] and the heavier mass particle is [tex]M[/tex].
Now, by momentum conservation and energy conservation:
[tex]mv = mv_{m} + Mv_{M}[/tex]
[tex]mv^{2} = mv^{2}_{m} + Mv^{2}_{M}[/tex]
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.
[tex]v_{m} = v\frac{m - M}{m + M}\\\\\\v_{M} = v\frac{m + M}{m + M}\\[/tex]
So now, we see that [tex]v_{m} < 0[/tex] and [tex]v_{M} > 0[/tex]. So therefore, the smaller mass recoils out.
Hope this helps you!
Bye!
