Bouncy ball: A ball is dropped from a height of H meters. Under ideal conditions (vacuum), after each bounce it returns to 1/3 of its previous height. (i) To what height does the ball rise after it hits the floor for the n-th time? How long does it take to completely stop? (ii) Find the total vertical distance the ball travels before coming to rest.

i) , ii)

Explanation:

i) After each bounce, two thirds of previous energy is lost by the ball. Then, the height observes a geometric progression which is described herein:

Where n is the number of bounces.

ii) The total vertical distance that ball travels before coming to rest is:

the independent variable, or the one that is intentionally manipulated is the speed.