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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Arithmetic Progression and Geometric Progression

A ball is dropped from a height of 16 m and after each bounce rises to half of the previous height. Taking the initial drop plus all subsequent rises and falls, what is the total distance travelled before it comes to rest?

The total distance is 48 metres. The first fall is 16 m, and the later rises and falls form a GP 8, 4, 2 and so on, each counted twice, giving 2 times 16, which is 32 m. Adding 16 gives 48 m.

  1. A32 m
  2. B48 mCorrect
  3. C64 m
  4. D96 m

Explanation

Initial fall is 16 m. Each bounce then adds a rise and an equal fall: 2(8 + 4 + 2 + ...) = 2 x 8/(1 - 1/2) = 32 m. Total = 16 + 32 = 48 m. Choosing 32 m ignores the initial drop.

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