Geometric Progression: Ball Bouncing Distance Calculation | Homework Solution

[Chewy0087]

Homework Statement

A ball is dropped vertically from height h onto a flat surface, after the nth bounce it returns to high h / 3^n. Find the total distance traveled by the ball.

Homework Equations

Sum (infinity) = $$\frac{a}{1 - r}$$

The Attempt at a Solution

I don't see the problem,

r is 1/3, a is h,

$$\frac{h}{ 2/3 }$$= 1.5h, however the problem is I'm told the answer is 2h.

Any help would be appreciated

 

[CompuChip]

If it bounces to height h/3^n, it will also have to drop to the ground from height h/3^n again. So it always travels this distance twice, except when n = 0.

 

[Chewy0087]

Gotcha, thank you.