A ball of mass `m` moving with velocity `u` strikes another identical ball at rest. Find the velocities of the balls after the collision if the coefficient of restitution is `e` and the collision is head -on. Also , calculate the loss in `K.E.`

Explanation

By the momentum conservation
`mu + m xx 0 = mv_(1) + mv_(2)` (i)
`v_(1) - v_(2) = -e (u_(1) - u_(2))` (ii)
From (i)
`v_(1) + v_(2) = u` (iii)
From (ii)
`v_(1) - v_(2) = -eu` (iv)
Solving , `v_(1) = ((1 - e)/(2)) u , v_(2) = (( 1 + e)/(2))u`
Loss in `K.E.,Delta K = (1)/(2) (m_(1) m_(2))/((m_(1) + m_(2))) ( u_(1) - u_(2))^(2) ( 1 - e^(2))`
`= (1)/(4) mu^(2) ( 1- e^(2))`