Two ball bearing of mass m each moving in opposite directions with equal speeds v collide head on with each other. Predict the outcome of the collision, assuming it to be perfectly elastic.

Explanation

`m_(1)=m_(2)=m` (say)
`u_(1)=v,u_(2)=-v`
As the collision is perfectly elastic velocities after the collision will be
`v_(1)=(m_(1)-m_(2))/(m_(1)+m_(2))u_(1)+(2m_(2))/(m_(1)+m_(2))u_(2)`
`=(m-m)/(m+m).v+(2m)/(m+m)(-v)`
`=0-v=-v`
`v_(2)=(2m_(1))/(m_(1)+m_(2)).u_(1)+(m_(2)-m_(1))/(m+m).u_(2)`
`=(2m)/(m+m).v+(m-m)/(m+m)(-v)`
`implies v+0=v`
Thus the two balls bounce back with equal speeds after the collision.