We might think that a ball that is dropped from a height of 14 feet and rebounds to a height 3/4 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.

A. Show that a ball dropped from a height $h$ feet reaches the floor in ${1\over4}\sqrt{h}$ seconds. Then use this result to find the time, in seconds, the ball has been bouncing when it hits the floor for the first, second, third and fourth times:
time at first bounce =
time at second bounce =
time at third bounce =
time at fourth bounce =

B. How long, in seconds, has the ball been bouncing when it hits the floor for the $n$th time (find a closed form expression)?
time at $n$th bounce =

C. What is the total time that the ball bounces for?
total time =