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Math Help - Related Rate Problems

  1. #1
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    Related Rate Problems

    I'm stuck on this related rate problem.

    A water skier skis over a ramp that is 15 ft long and 4 ft high, at a speed of 30 ft/s. How fast is she rising as she leaves the ramp?
    Last edited by Kari; October 19th 2008 at 07:15 PM.
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  2. #2
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    This is what I calculated please tell me if its right or wrong.

    Given: x^2+y^2=z^2, dz/dt=30ft/s, x=15, y=4
    Unknown: z, dx/dt, dy/dt

    x^2 + y^2 = z^2
    15^2 + 4^2 = z^2
    z = √241

    To get the 30 ft/s, multiply sides of the triangle by 30/√241.
    So, 15*30/√241 and 4*30/√241 => dx/dt = 450/√241 and dy/dt = 120/√241

    So Chain rule: x^2 + y^2 = z^2 => 2x*dx/dt + 2y*dy/dt = 2z*dz/dt

    2(15)*450/√241 + 2(4)120/√241 = 2(√241)30

    13500/√241 + 960/√241 = 60/√241
    =>60/√241 = 60/√241

    So she's rising at a rate of 60√241 ft/s.
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