A ball is dropped from a height of 10 feet and bounces. Each bounce is 3/4 of the height of the bounce before. Thus, after the ball hits the floor for the first time, the ball rises to a height of 10(3/4)=7.5 feet, and after it hits the floor for the second time, it rises to a height of 7.5(3/4)=10(3/4)^2=5.625 feet. (Assume g=32 ft/sec^2 and that there is no air resistance.)a) Find an expression for the height, hn to which the ball rises after it hits the floor for the nth time. State answer in terms of feet. b) Find an expression for the total vertical distance Di the ball has traveled when it hits the floor for the first, second, third, and fourth times (i=1, 2, 3, 4). Round the answer to 2 decimal places. c) Find an expression for the total vertical distance Dn the ball has traveled when it hits the floor for the nth time. Express your answer in closed-form.