Question

A bouncy ball is released from a certain height. On the first bounce, it travels 32cm. With each subsequent bounce, it travels 9/10 the distance of the previous bounce. What is the total distance that the ball has traveled when it completes its 25th bounce?

Answer 1

594?

Explanation:

The wording leaves a little to be desired. What does that 32 actually mean?

I don't think it is asking us to add on the distance it has to travel to get a bounce of 32. We are starting with a bounce that is 32 high.

The second bounce is 9/10 of that height which turns out to be 28.8.

The third bounce is 9/10 of 28.8 which is 25.92, I think, and then it continues on.

So here are the Givens

Given

a = 32

r = 9/10

n = 25

Formula

Sum = a(1 - r^n) / (1 - r)

Solution

Sum = 32*(1 - (9/10)^25) / (1 - 9/10)

Sum = 32*(1 - 0.07179) / ( 1 - 9/10)

Sum = 32*(0.9282) / 0.1

Sum = 29.7 / 0.1

Sum = 297

But that number represents only the distance going up. You must also take the distance going down. You have to double this answer.

2*sum = 2 * 297

Sum' = 594

================

The wording is a real snake. We don't really know if we need to include some height that was a start. If we do, the answer is 594 + k where k is a constant yet to be determined. Usually k is part of the problem.

Or do we take a = 32 as the first drop? We can't tell from the wording.