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May 30, 2015

Homework Help: Calculus

Posted by Sandy on Wednesday, April 15, 2009 at 9:55am.

A ball is dropped from a height of 10 feet and bounces. Each bounce is Ę˙ 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(Ę˙ ) = 7.5 feet, and after it hits the second floor for the second time, it rises to a height of 7.5(Ę˙ ) = 10(Ę˙ )ę¸ = 5.625 feet. (Assume g= 32 ft/sec ę¸ 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.
(b) Find an expression for the total vertical distance the ball has traveled when it hits the floor for the first, second, third, and fourth times.
(c) Find an expression for the total vertical distance the ball has traveled when it hits the floor for the nth time. Express your answer in closed-form.

For part (a) I got ar^n
For part (b) I got
1st bounce = a + ar
2nd bounce = a + ar + ar + arę¸
3rd bounce = a + ar+ ar + arę¸ + arę°
4th bounce = a + ar +ar + arę¸ + arę° + arę° + arę¨
For part (c) I do not kow what to do any help would be greatly appreciated.

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