(a)[2]
Demonstrate that the speed of $P$ when it is $20\,\text{m}$ above the ground is $15\,\text{m s}^{-1}$.
(b)[2]
At the instant $P$ is $20\,\text{m}$ above the ground, it collides with a second particle $Q$ of mass $0.1\,\text{kg}$ moving downwards at $20\,\text{m s}^{-1}$. The collision leaves $P$ momentarily at rest. Find the velocity of $Q$ immediately after impact.
(c)[6]
When $P$ strikes the ground, it rebounds straight upwards with half the speed it had immediately before impact. Determine the height above the ground where $P$ and $Q$ next meet.