A ball is dropped from a height of 15 feet and bounces. Suppose that each bounce is 5/8 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of 15(§) = 9.375 feet, etc. (Assume g = 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 nth time: h₁ = 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 nth time. D₁ =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A ball is dropped from a height of 15 feet and bounces. Suppose that each bounce is 5/8 of the height of the bounce before. Thus, after the ball hits the floor for
the first time, it rises to a height of 15(§ ) = 9.375 feet, etc. (Assume g = 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 nth time:
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 nth time.
D₂
=
Transcribed Image Text:A ball is dropped from a height of 15 feet and bounces. Suppose that each bounce is 5/8 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of 15(§ ) = 9.375 feet, etc. (Assume g = 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 nth time: 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 nth time. D₂ =
Find the sum of each of the geometric series given below. For the value of the sum, enter an expression that gives the exact value, rather than entering an
approximation.
5
4 42
A.-20+55 +
Β. Σ (;)" =|
n=3
5
43
+ +56
Transcribed Image Text:Find the sum of each of the geometric series given below. For the value of the sum, enter an expression that gives the exact value, rather than entering an approximation. 5 4 42 A.-20+55 + Β. Σ (;)" =| n=3 5 43 + +56
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