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Math Help - height, time, speed

  1. #1
    Senior Member furor celtica's Avatar
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    height, time, speed

    this has to do with diffrentiation and not kinematics
    a boy stands on the edge of a cliff of height 60m. he throws a stone vertically upwards so that its distance h metres above the cliff top is given by h=20t -5(t^2)
    a. calculate the max height of the stone above the cliff top
    i differentiated h=f(t) and got 20m
    b. calculate the time which elapses before the stone hits the beach (it just misses the boy on the way down (lucky him))
    i took h=-60 and got t=6
    c. calculate the speed with which the stone hits the beach.
    here i'm lost. shouldnt speed=f'(t)=20-10t? but i know this is wrong cos the answer is 40ms^-1
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  2. #2
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    You are pretty much right. f'(t) = 20 - 10t. Plug in t= 6 to get 20 - 60 =-40 m/s. This is the velocity. The speed is the magnitude of the velocity, which is |-40| = 40 m/s.
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  3. #3
    Senior Member furor celtica's Avatar
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    oh good point thats why its negative
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