Collision with a vertical spring

 

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

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 $ m/s$^2$.