Mathematics

Problem

A ball is dropped from a height of

2\,\text{m}

. After each bounce it rises to

60\%

of the height from which it fell. Ignoring the radius of the ball, calculate the total vertical distance it travels before coming to rest. a)

6.5\,\text{m}

8\,\text{m}

5\,\text{m}

10\,\text{m}

Intuitive explanation

The key insight is to split the ball's journey into two parts: the initial drop, and then an infinite series of bounces. Each bounce goes up to 60% of the previous height, then falls back down that same distance—so you're summing both ascents and descents. This is a geometric series problem in disguise: once you recognize the pattern of heights, you can use the formula for an infinite geometric sum to find the total distance without adding infinitely many terms.

Intuitive explanation

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