Urgen help on this math question. thank you so much.?

Question

a ball is dropped from a height of 10 meters. Each time it strikes the ground it bounces vertically to a height that is 3/4 of the previous height. Find the total distance the ball will travel if it is allowed to bounce indefinitely

express in term of integral. thank you so much

Answer 1

The mathematics at the link below are complex but they may help you get to where you want to be. That's the bouncing ball problem.