Two balls, Ball A with mass m and Ball B with mass $6$m$,$ are suspended by light

strings of length L$.$ Ball B is initially hanging at rest. Ball A is pulled back to horizontal

then released from rest. After Ball A hits Ball B$,$ it bounces backward to the left with

half the speed it had just before the collision.

Determine the maximum height reached by Ball B above its initial position in terms of L$.$