Question

A ball is thrown from point A, it reaches to a height of x metres and after it bounces on to the land and raises to half the height. Given that it bounces half the height of the previous height. Find the product of first 9 heights. [4 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Let the height reached before first bounce $=xm$

Height reached after first bounce $=\frac{x}{2}$

Height reached after second bounce $=\frac{x}{4}=\frac{x}{2^2}$

Height reached after third bounce $=\frac{x}{8}=\frac{x}{2^3}$

Height reached after fourth bounce $=\frac{x}{16}=\frac{x}{2^4}$

Height reached after fifth bounce $=\frac{x}{32}=\frac{x}{2^5}$

Height reached after sixth bounce $=\frac{x}{64}=\frac{x}{2^6}$

Height reached after seventh bounce $=\frac{x}{128}=\frac{x}{2^7}$

Height reached after eight bounce $=\frac{x}{256}=\frac{x}{2^8}$

$\therefore$ Product of first 9 heights $=\frac{x^9}{2^{36}}$