A small disc of mass $60\mathrm{g}$ is placed on top of a vertical spring, which can oscillate and has a spring constant $k = 6\mathrm{N/m}$. Initially the spring is at rest. From a distance $h = 0.8\mathrm{m}$ above the spring we release a small elastic bouncing ball of mass $10\mathrm{g}$.

The ball collides with the disc with a coefficient of restitution $e = \frac{3}{4}$ and bounces back - up.

Find the maximum distance between the ball and the disc.

Possible extension: What about the maximum distance between the ball and the disc after the two objects have collided a second time? (Computationally heavy!)

For simplicity, you may assume that $g = 10 \mathrm{m/s}^2$.