A tennis ball with (small) mass m 2 , sits on the top of a basketball with (large) mass m 1 . The bottom of…

Just before the collision, the velocity of the basketball in the downward direction is $\sqrt{2gh}$ and just after the collision its velocity reverses its direction

So just after the collision, the downward moving tennis ball collides with upward moving basketball. The velocity of the tennis ball after this collision is

$$\begin{gathered} v=-\left(-2\sqrt{2gh}\right)+\sqrt{2gh} \\ \Rightarrow v=3\sqrt{2gh} \end{gathered}$$

The height up to which the tennis ball will bounce is

$$\begin{gathered} h^{\text{'}}=\frac{{\left(3\sqrt{2gh}\right)}^2}{2g} \\ \Rightarrow h^{\text{'}}=9h \end{gathered}$$