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Related Rate Bungee Problem Question

  1. Oct 30, 2009 #1
    1. The problem statement, all variables and given/known data

    A bungee jumper has reached a point in her exciting plunge where the taut cord is 100 feet long with a 1/2 inch radius and stretching. She is still 80 feet above the ground and is now falling at 40 feet per second. You are observing her jump from a spot on the ground 60 feet from the potential point of impact.

    - From your observation point, at what rate is the angle of elevation to the jumper changing?

    So, without a diagram, x=60, y= 80 and you have to solve for dΘ/dt. So the hypotenuse value would be 100 at this moment.

    My Question: I understand mostly the implicit differentiation, but Why when I solve for dΘ/dt, i need to use the 100 feet for hypotenuse? Isn't the hypotenuse changing?

    3. The attempt at a solution

    My equation for this question is sinΘ=y/100 . But why do I use 100 if it is changing?
     
  2. jcsd
  3. Oct 30, 2009 #2

    LCKurtz

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    You shouldn't use the 100 for the equation. You have x = 60 (constant), y is variable, and the hypotenuse h = sqrt(y2+ 602). So as y varies, h varies as you have observed. So your equation that you differentiate with respect to time should be:

    [tex]y = h\sin{\theta} = \sqrt{y^2 + 60^2}\ \sin\theta[/tex]

    Differentiate that for the related rate equation and put your "snapshot values" in the resulting related rates equation.
     
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