A ball is released from a height of x meters. Given that it bounces back to half of its original height. Find the product of heights after eight bounces. [4 MARKS]
Formula: 1 Mark
Application: 1 Mark
Answer: 2 Marks
Given that
The ball is released from a height of x m
Height reached after first bounce =x2
Height reached after second bounce =x4=x22
Height reached after third bounce =x8=x23
Height reached after fourth bounce =x16=x24
Height reached after fifth bounce =x32=x25
Height reached after sixth bounce =x64=x26
Height reached after seventh bounce =x128=x27
Height reached after eight bounce =x256=x28
∴ Product of first 9 heights =x×x2×x22×x23×x24×x25×x26×x27×x28
=x(1+1+1+1+1+1+1+1+1)2(1+2+3+4+5+6+7+8)
(∵ab×ac = ab+c)
=x9236
The product of heights after 8 bounces =x9236