Question

A ball was dropped from a height of 10 feet. Each time it hits the ground, it bounces 4/5 of its previous height. Find the total distance traveled by the bouncing ball.

Answer 1

d = 90 ft

Step-by-step explanation:

As we know that after each bounce it reaches to 4/5 times of initial height

so we can say

`h_2 = (4)/(5)h`

so the distance covered is given as

`d = h + 2((4)/(5)h) + 2((4)/(5))^2h + 2((4)/(5))^3h........`

here we know that

h = 10 feet

`d = h + 2((4)/(5)h)(1 + (4)/(5) + ((4)/(5))^2 + ...........)`

`d = 10 + 2((4)/(5)(10))((1)/(1 - (4)/(5)))`

`d = 90 ft`