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Related Rates (similar triangles)

  1. Oct 30, 2009 #1
    1. The problem statement, all variables and given/known data
    A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 ft from the base of the pole?

    2. Relevant equations
    http://imageiso.com/out.php/i26481_Relatedrates.JPG [Broken]

    18/x = 6(x-y)

    3. The attempt at a solution

    y=30 ft

    simplified 12x=18y

    tip of shadow will be at 45 ft

    d/dt 12x = d/dt 18y

    dx/dt 12 = dy/dt 18

    if i plug the 8ft/s as my dx/dt i get a dy/dt of 16/3ft/s

    but that cant be the right answer since i didnt use the 30ft given in my original question

    where am i going astray?
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Oct 30, 2009 #2


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    You aren't going astray. Think about the fact that maybe the speed of the tip of the shadow only depends on how fast she is moving, and not where she happens to be.
  4. Oct 31, 2009 #3
    if what you said is true, than for some reason my answer of 16/3 isnt correct (its online so i get my answers right away if i am correct)

    i still dont get whats wrong...

    a little more insight will be greatly appreciated
  5. Oct 31, 2009 #4


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    Your analysis is fine. You just plugged your 8 feet/sec in for the wrong variable. It is dy/dt that is 8 and dx/dt you are seeking.
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