Two particles of masses `m` and `2m` moving in opposite directions collide elastically with velocity `2v` and `v`, respectiely. Find their velocities after collision.

Explanation

Let the final velocities of mass `m` and `2m` be `v_(1) and v_(2)` respectively as shown in figure.

By conservation of momentum, we get
`m(2v)+2m(-v)=m(v_(1))+2m(v_2)`
or `0=mv_(1)+2mv_(2)`
or `v_(1)+2v_(2)=0`
and since the collision is elastic
`v_(2)-v_(1)=2v-(-v)`
or `v_(2)-v_(1)=3v`
Solving the above two equations we get
`v_(2)=v` and `v_(1)=-2v`
That is mass `2m` returns with velocity `v` while mass `m` returns with velocity `2v` in the direction shown in figure.