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Related rates, check my answer pls

  1. Aug 25, 2012 #1
    1. The problem statement, all variables and given/known data
    A highway patrol plane is flying 1 mile above a long, straight road, with constant ground speed of 120 m.p.h. Using radar, the pilot detects a car whose distance from the plane is 1.5 miles and decreasing at a rate of 136 m.p.h. How fast is the car traveling along the highway?


    3. The attempt at a solution

    work.jpg
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 25, 2012 #2

    Dick

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    It's wrong. The value of x in the related rates equation is not an unknown. x^2+1=1.5^2. It's easy to find. And 'x' is the distance, not a velocity. dx/dT is not -120. It's a combination of the plane's velocity with the unknown velocity of the car. That's what you want to solve for.
     
    Last edited: Aug 25, 2012
  4. Aug 26, 2012 #3
    So would you say that (velocity of car)[itex]\frac{dc}{dt} = 120 + \frac{dx}{dt}[/itex]

    so that

    [itex]\frac{dh}{dt}=\frac{x}{\sqrt{x^2+1}}\frac{dx}{dt}[/itex]

    where

    [itex]\frac{dx}{dt} = \frac{dc}{dt} - 120[/itex]

    [itex]\frac{dh}{dt}= -136[/itex]

    and

    x=[itex]\sqrt{1.25}[/itex]

    so that [itex]\frac{dc}{dt} \approx -62.46 \approx 62.46 mph[/itex]
     
    Last edited: Aug 26, 2012
  5. Aug 26, 2012 #4

    Dick

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    Yes, I think that's more like it.
     
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