A ball strikes directly upon another ball at rest and is itself reduced to rest by the impact. If half of the initial `K.E.` is lost in collision, find the value of `e`.

Explanation

`m_(1) u + m_(2) xx 0 = m_(1) xx 0 + m_(2) v`
`m_(1) u = m_(2)v` (i)
`v_(1) -v_(2) = -e(u_(1) - u_(2))`
`v = eu` (ii)
From (i) and (ii)
`m_(1) u = m_(2) v = m_(1) e u`
`m_(1) = m_(2) e`
`Delta K = (1)/(2) K_(i)`
`(1)/(2) (m_(1) xx m_(2))/(m_(1) + m_(2)) (u - 0)^(2) ( 1 - e^(2)) = (1)/(2) xx (1)/(2) m_(1) u^(2)`
`(m_(2))/(m_(1) + m_(2)) (1 - e^(2)) = (1)/(2)`
`(m_(2))/(m_(2)e + m_(2)) (1 - e^(2)) = (1)/(2)`
` 1 - e = (1)/(2) rArr e = (1)/(2)`