A ball is dropped from a height of 10 feet and bounces.Each bounce is 34 of the height
Chapter 9, Problem 46(choose chapter or problem)
A ball is dropped from a height of 10 feet and bounces.Each bounce is 34 of the height of the bounce before.Thus, after the ball hits the floor for the first time, theball rises to a height of 10( 34 )=7.5 feet, and after ithits the floor for the second time, it rises to a height of7.5( 34 ) = 10( 34 )2 = 5.625 feet. (Assume that there is noair resistance.)(a) Find an expression for the height to which the ballrises after it hits the floor for the nth time.(b) Find an expression for the total vertical distance theball has traveled when it hits the floor for the first,second, third, and fourth times.(c) Find an expression for the total vertical distance theball has traveled when it hits the floor for the nthtime. Express your answer in closed form.
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