In the previous problem , if the collision is head - on elastic , find (a) the velocities of balls immediately after the collision and (b) the maximum height attained by eacl ball.

Explanation

(a)
By the momentum conservation
`m sqrt(2g L) + 2m xx 0 = m v_(1) + 2 mv_(2)` (i)
`v_(1) + sqrt(2 gL) = v_(2) + 0` (ii)
Solving , `v_(1) = -(1)/(3) sqrt( 2gL), v_(2) = (2)/(m) sqrt(2 gL)`
(b)
`0 = v_(1)^(2) - 2gh_(1) rArr 0 = (1)/(9) xx 2gL - 2gh_(1)`
`rArr h_(1) = (L)/(9)`
`0 = v_(2)^(2) - 2gh_(2) rArr 0 = (4)/(9) xx 2 g L - 2gh_(2)`
`rArr h_(2) = (4L)/(9)`