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Implicit differentiation help

  1. Apr 10, 2007 #1
    1. The problem statement, all variables and given/known data
    A spotlight on the ground shines on a wall 14m away. If a dog, 0.5m tall, runs from the spotlight towars the building at a speed of 1 m/s, how fast is the height of the animal's shadow on the building decreasing when the dog is 5 meters from the building?

    Wrt = with respect to
    2. Relevant equations
    Pythagoreon theorem, implicit differentiation, you name it.


    3. The attempt at a solution

    Knowing that Dc/dt is canine wrt time is 1 m/s and i am trying to find dh/dt 'h' for height wrt time

    and im stuck....
    .
    ..
    ...
    14^2 + wall^2 = Hyp^2
     
  2. jcsd
  3. Apr 10, 2007 #2
    This is called a "related rates" problem, not "implicit differentiation."

    dc/dt? if you're using the pythagorean theorem, that implies (at least to me) that the dog is running on the hypotenuse??

    At a glance, I'm having a tough time getting the pythagorean theorem to really work for me on this problem. Have you thought about the angle made by the flashlight between the ground and the beam to the top of the dog? Or, have you thought about similar triangles?
     
  4. Apr 11, 2007 #3

    HallsofIvy

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    You should have put "similar triangles", not "Pythagorean theorem", in "Relevant Equations". Can you draw a picture and see why?
     
  5. Apr 11, 2007 #4
    Here i go furthering my development in related rates
    let l be length of shadow and let x be ground covered with light
    2/L = X/12
    24=LX
    L=24X^-1
    dL/dt(1)=-24X^-2
    dL/dt=-24(12-8)^-2
    dL/dt=9/32
     
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