A ball is dropped from a height of 8 feet and bounces. Suppose that each bounce is 3/4 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of 8(3/4) = 6 feet, etc. (Assume g = 32 ft/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: 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: 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.
A ball is dropped from a height of 8 feet and bounces. Suppose that each bounce is 3/4 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of 8(3/4) = 6 feet, etc. (Assume g = 32 ft/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: 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: 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.
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 6ECP: The resistance of a copper wire carrying an electrical current is directly proportional to its...
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A ball is dropped from a height of 8 feet and bounces. Suppose that each bounce is 3/4 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of 8(3/4) = 6 feet, etc. (Assume g = 32 ft/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:
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:
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.
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Transcribed Image Text:A ball is dropped from a height of 8 feet and bounces. Suppose that each bounce is 3/4 of the
height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height
of 8( 3 ) = 6 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 n
th 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.
Dn
=
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