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    • M
      modestwallaby M2★ M3★ M4★ M5
      last edited by

      A solid rubber ball rebounds to three-fourths the height it is dropped from. What is the total vertical distance traveled by a ball dropped from a height of 24 feet as it bounces to rest?

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      • C
        contentamphibian @modestwallaby
        last edited by

        24+3/4(24)(2)+(3/4^2)(24)(2)+(3/4^3)(24)(2)+.....
        (The x2 is because the ball drops the same distance up and down)

        This is an infinite arithmetic sequence.

        Let S = 3/4(24)(2)+(3/4^2)(24)(2)+... = 36+(3/4)(36)+(3/4^2)(36)+....
        So 4/3S=48+36+(3/4)(36)+....
        So 4/3S-S=1/3S=48
        So S=144
        So S+24=168?

        Contentamphibian

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