We might think that a ball that is dropped from a height of 15 feet and rebounds to a height 5/8 of its previous height at each bounce keeps bouncing forever since it takes infinitely many bounces. This is not true! We examine this idea in this problem.
Show that a ball dropped from a height h feet reaches the floor in ¼ √h seconds. Then use tins result to fmd the tune, in seconds, the ball has been bouncing when it hits the floor for the first, second, third and fourth times:
How long, in seconds, has the ball been bouncing when it hits the floor for the 71th time (find a closed form expression)?
What is the total time that the ball bounces?