Question

A tennis ball with (small mass $m_2$ rests on the top of a basketball of mass $m_1$ which is at a height h above the ground, and the bottom of the tennis ball is at height h + d above the ground. The balls are dropped. The tennis ball bounces to a height of d+xh with respect to ground. Find the value of x.
(Assume all collisions to be elastic and $m_1$ >> $m_2$)

Answer 1

At the moment when the basketball strikes the ground,

$v_b=\sqrt{2gh}$ , the direction is downwards but is instantaneously reversed on striking the ground.

The centre of mass of the tennis ball also falls by $h$.

$v_t=\sqrt{2gh}$ downwards.

The velocity of the tennis ball after collision is $3\sqrt{2gh}$

Height to which the ball rises is $d+9h$ .