Bodacious Bouncing Basketball

[BMAD]

A basketball is dropped straight down from the rim height of 10 feet. Each bounce, it rises to the same percentage (p%) of its previous height. The ball finally comes to rest after traveling a total of 70 (vertical) feet. What is the mystery "rebound" percentage p?

[bonanova]

Let f be the fractional rebound height.

Distance = 10 + 10f + 10f + 10f² + 10f² + 10 f³ + 10f³ + ... = 70.

20 x Sum(i=0, inf) fⁱ = 20/(1-f) = 80.

(1-f) =1/4

f = 0.75.

p = 75%.