We might think that a ball that is dropped from a height of 6 feet and rebounds to a height 7/8 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. a)show that a ball dropped from a height h feet reaches the floor in 1/4(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: first bounce=second bounce=third bounce=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 =