Math 2020 logic geo #2..

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thanks for the help with the first problem this is the last problem I have a question on...

A superball rebounds half the height it drops. The ball is dropped from a height of 176 feet. How far off the ground is the ball when it has traveled a total of 500 feet?

  • Math 2020 logic geo #2.. -

    You do not say if you know about geometric series so with brute force:
    It goes down 176 feet and bounces
    total = 176
    The first bounce up is 176/2 = 88 feet
    total = 264
    Then it also goes down 88 feet
    total =352
    then up 44
    total = 396
    then down 44
    total = 440
    then up 22
    total = 462
    then down 22
    total = 484
    then up 11
    total = 495 when it is 11 feet high
    then down 5 to reach 500
    Leaving it 6 feet high.

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