A ball is dropped from a height of 14 feet and bounces. Suppose that each bounce is 3/4 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of $14 ({3\over 4}) = 10.5$ feet, etc. (Assume $g = 32 \hbox{ft/s}^2$ and no air resistance.)

A. Find an expression for the height, in feet, to which the ball rises after it hits the floor for the $n$th time:
$h_n =$

B. Find an expression for the total vertical distance the ball has traveled, in feet, when it hits the floor for the first, second, third and fourth times:
first time: D =
second time: D =
third time: D =
fourth time: D =

C. Find an expression, in closed form, for the total vertical distance the ball has traveled when it hits the floor for the $n$th time.
$D_n =$