A ball is dropped from a height of 20 feet and bounces. Suppose that each bounce is 7/8 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of 20(78)=17.520(78)=17.5 feet, etc. (Assume g=32ft/s2g=32ft/s2 and no air resistance.) A. Find an expression for the height, in feet, to which the ball rises after it hits the floor for the nnth time: hn=hn= B. Find an expression for the total vertical distance the ball has traveled, in feet, when it hits the floor for the first, second, third and fourth times: first time: D = second time: D = third time: D = fourth time: D = C. Find an expression, in closed form, for the total vertical distance the ball has traveled when it hits the floor for the nnth time. Dn=
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A ball is dropped from a height of 20 feet and bounces. Suppose that each bounce is 7/8 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of 20(78)=17.520(78)=17.5 feet, etc. (Assume g=32ft/s2g=32ft/s2 and no air resistance.)
A. Find an expression for the height, in feet, to which the ball rises after it hits the floor for the nnth time:
hn=hn=
B. Find an expression for the total vertical distance the ball has traveled, in feet, when it hits the floor for the first, second, third and fourth times:
first time: D =
second time: D =
third time: D =
fourth time: D =
C. Find an expression, in closed form, for the total vertical distance the ball has traveled when it hits the floor for the nnth time.
Dn=
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