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Math Help - [SOLVED] Rates of Change Problem

  1. #1
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    Exclamation [SOLVED] Rates of Change Problem

    From a platform tower 10 m high, a diver performs a handstand dive.
    His height, h, in metres above the water at t seconds can be modelled by
    h(t) = 10 - 4.9t^2. Estimate the rate at which the diver enters the water.

    The answer is supposed to be -14m/s i just don't understand how to get to that answer. At first a solution seemed simple, but i got the wrong answer.

    Thanks in advanced, Joe
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  2. #2
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    First find the time taken for the diver to fall. Find t when h=0:

     h(t) = 10 - 4.9t^2
     0 = 10 - 4.9t^2
     10 = 4.9t^2
     t = \sqrt {\frac{10}{4.9}}

    to find the rate at which the diver enters the water (speed) differentiate:

     v(t) = -9.8t

    Then find the speed for the value of t found:

     v(t) = -9.8*\sqrt {\frac{10}{4.9}}
     = -14m/s
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