Answer
The proof is below.
Work Step by Step
We know that the velocity of the balls when they hit the ground is:
$Mgh=\frac{1}{2}Mv^2\\ v=4.42\sqrt{h}$
We know the following equation for elastic collisions:
$v_{1f}=\frac{m_1-m_2}{m_1+m_2}v_{1i}+\frac{2m_2}{m_1+m_2}v_{2i}$
Since the large mass is much more massive and the velocities are initially equal, this becomes:
$v_{1f}=v+2v=3v$
Thus, we find:
$gh_f=\frac{1}{2}176.58h$
$h_f=9h$
