We might think that a ball that is dropped from a height of 8 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 nth time (find a closed form expression)? time at nth bounce =c. what is the total time that the ball bounces for? total time =