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A rubber ball is dropped from a height of 729 feet, and at each bounce it rebounds one-third of the height from which it last fell. How far has the ball travelled by the time it strikes the ground for the 5th time?

  • math -

    first time: 729/3=243
    second time: 243/3
    third time:81/3
    fourth time: 27/3
    fifth time: 9/3=3ft

  • math -

    distance for 1st bounce = 729
    distance for 2nd bounce = 2(1/3)(729) = 2(243)
    distance for 3rd bounce = 2(1/3)(243) = 2(81)
    distance for 4th bounce = 2(1/3)(81) = 2(27)
    distance for 5th bounce = 2(1/3)(27) = 2(9)

    total distance
    = 729 + 2(243+81+27+9) = 1449

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