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Math Help - [SOLVED] Work

  1. #1
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    [SOLVED] Work

    A bucket is being lifted to 20 ft in the air and starts with off 16lbs of water and is leaking at a constant rate. It finishes draining just as it reaches the top. How much work was spent lifting the water alone? (find the proportion of water left at elevation x ft)

    the answer is 160 lbs ft but I got 3200
    3200/4= 160 but I don't see how that would fit from the given information
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  2. #2
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    Quote Originally Posted by TAG16 View Post
    A bucket is being lifted to 20 ft in the air and starts with off 16lbs of water and is leaking at a constant rate. It finishes draining just as it reaches the top. How much work was spent lifting the water alone? (find the proportion of water left at elevation x ft)

    the answer is 160 lbs ft but I got 3200
    3200/4= 160 but I don't see how that would fit from the given information
    weight of water is changing at the rate of -\frac{16}{20} = -\frac{4}{5} lbs/ft

    F = 16 - \frac{4}{5}h<br />

    W = \int_0^{20} 16 - \frac{4}{5}h \, dh

    W = \left[16h - \frac{2h^2}{5}\right]_0^{20}

    W = 16(20) - \frac{2(20^2)}{5} = 320 - 160 = 160 ft-lbs
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