A ball was dropped from a height of 6 feet and began bouncing. The height of each bounce was three-f

Discussion in 'Calculator Requests' started by math_celebrity, Oct 26, 2020.

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    A ball was dropped from a height of 6 feet and began bouncing. The height of each bounce was three-fourths the height of the previous bounce. Find the total vertical distance travelled by the all in ten bounces.

    The height of each number bounce (n) is shown as:
    h(n) = 6(0.75)^n

    We want to find h(10)
    h(n) = 6(0.75)^n

    Time Height
    0 6
    1 4.5
    2 3.375
    3 2.53125
    4 1.8984375
    5 1.423828125
    6 1.067871094
    7 0.8009033203
    8 0.6006774902
    9 0.4505081177
    10 0.3378810883

    Adding up each bounce from 1-10, we get:
    16.98635674

    Since vertical distance means both up and down, we multiply this number by 2 to get:
    16.98635674 * 2 = 33.97271347

    Then we add in the initial bounce of 6 to get:
    33.97271347 + 6 = 39.97271347 feet
     

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