 Solution

As $m_1/m_2\to 0$, a gives $v_1\to 3u$. The upper ball then rises through height $v_1^2/(2g)$ above the near-ground mutual encounter:The rise above its original release level is therefore $8H$ in this idealization. Although its speed triples, the light ball's fraction of the total energy tends to zero, $f(r)\sim 9r$. This distinguishes maximum rebound height from the maximum energy-transfer fraction in b. With finite radii, $9H$ is the leading approximation in drop height relative to the collision height.