Question

A ball was dropped from a height of 60m. Each time it hit the ground, it bounced up 1/2 (half) of the height that it dropped. How far had the ball travelled when it hit the ground for the fifth time?

Answer 1

The ball traveled 116.25 m when it hit the ground for the fifth term

Explanation:

This is a geometric progression exercise and what we are asked to look for is the sum of a GP.

The ball was dropped from a height of 60 m. This means that the initial height of the ball is 60 m.

First value, a = 60

Each time it hit the ground, it bounced up 1/2 (half) of the height that it dropped.

This is the common ratio, r = 1/2 = 0.5

The number of terms it hits the ground is the number of terms in the GP.

number of terms, n = 5

The distance traveled by the ball when it hit the ground for the fifth term will be modeled by the equation:

`S_n = (a(1 - r^n) )/(1 - r) \\S_5 = (60(1 - 0.5^5) )/(1 - 0.5)\\S_5 = (58.125)/(0.5) \\S_5 = 116.25 m`