A ball rebounds the ground to a height of 72 cm, and each time it rebounds to two thirds of the height. Estimate the total distance the ball travels before it comes to rest

Answer 1

counting the first bounce at up and down ...
we have
144 + 144(2/3) + 144(2/3)^2 + ...
which is an infinite geometric series where
a = 144 , r = 2/3
sum(all terms) = a/(1-r)
= 144/(1-2/3)
= 144/(1/3)
= 432 cm