Height of the balls after two bounces is
52/100 × (0.52 ×0.5) = 0.52 × 0.52 × 0.5
= 0.52^2 × 0.5 m
Therefore the series turns into 0.5,0.5(0.52),0.5(0.52)^2,....
So by finding the height f(n) after n bounces would be
f(n) = 0.5(0.52)^n-1
To get the height of the ball of the third path, we need to put n=3
f(3)= 0.5(0.52)^3-1
=0.5(0.52)^2
=0.14m
Answer: B ) 0.5 × (0.52)^n-1 ; 0.14m
