A bouncing ball and the coefficient of restitution

Three balls are dropped from $1.8\ \text{m}$ onto a hard floor: a bouncy one ($e = 0.9$), an average one ($e = 0.7$) and a dull one ($e = 0.5$). You will make the program find the height after each bounce, the bounce at which the average ball first rises less than $5\ \text{cm}$, and how far it travels in all.

The idea. Each bounce multiplies the speed by $e$, so it multiplies the height by $e^2$: $h_n = e^{2n}h_0$.

Your tasks.

1. Make heights(e) return the heights after bounces $0$ to $10$.
2. Find the first bounce at which the $e = 0.7$ ball rises less than $0.05\ \text{m}$.
3. Find the total distance the $e = 0.7$ ball travels in its first $10$ bounces (the first fall, then up and down after each bounce).