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math

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a student drop a rubber ball from a height of 8 feet . Each time the ball hits the ground, it bounces to 75% of its previous height.
a/ how far does the ball travel between tne second and third bounces .
b/ write an infinite series to model the total distance tralveled by the ball, excluding the distance traveled before the firstbounce

  • math - ,

    we have to count the up and the down of each bounce
    So from the moment of the first bounce:
    distance = 2(.75)(8) + 2(.75^2)(8) + 2(.75^3)(8) + ...
    = 16(.75) + 16(.75^2) + 16(.75^3) + ...
    so we have a GS, with
    a = 16 ,r = .75
    distance between 3rd and 2nd
    = 16(.75^2) - 16(.75^3) = 2.25 ft

    total distance = a/(1-r) = 16/(1-.75) = 64 ft

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