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 a second time, it rises to a height of 7.5(3/4) = 10(3/4)^2 = 5.625 feet. (Assume g = 32 ft/sec2 and that there is no air resistance.)

(a) Find an expression for the height to which the ball rises after it hits the floor for the nth time.

Find the total vertical distance, D, the ball has traveled when it hits the floor for the fourth time.

Question

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 a second time, it rises to a height of 7.5(3/4) = 10(3/4)^2 = 5.625 feet. (Assume g = 32 ft/sec2 and that there is no air resistance.) 

(a) Find an expression for the height to which the ball rises after it hits the floor for the nth time. 

 Find the total vertical distance, D, the ball has traveled when it hits the floor for the fourth time.

anonymous · Answer

hn=  10(3/4)^n    but i don't know how to find the total vertical distance, D

anonymous · Answer

I know part (a) but i dont know the second part

nubeer · Answer

hmm it says total distance when it hit the fourth time.. 
so u have to find the distance travelled during first 3 bounces..
when the ball dropped it travelled 10 feet then came back up 7.5 feet then went down 7.5 feet. then bounce again 5.625 feet up and then 5.625 down.. same way do for the next hit and aadd all distancees.

anonymous · Answer

thanks

nubeer · Answer

most welcome :)