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Derivatives, rates of change

  1. Dec 1, 2013 #1
    1. A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 5 fts along a straight path. How fast is the tip of his shadow moving when
    he is 40 ft from the pole?

    2. Relevant equations
    $$x^2+y^2=z^2$$
    3. The attempt at a solution

    I've drawn a diagram so far (I've attached it to this thread), but I don't know where to start. Can someone give me a hint?
     

    Attached Files:

  2. jcsd
  3. Dec 1, 2013 #2

    Simon Bridge

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    It would help to define some variables - let x=position of the man and y=position of the tip of his shadow.
    So, off your diagram, s=y-x.

    The question gives you dx/dt and asks you to find dy/dt.
    If you can find a relationship between x and y, then you can find dy/dt in terms of dx/dt just by differentiating.
    Hint: similar triangles.
     
    Last edited: Dec 1, 2013
  4. Dec 1, 2013 #3
    Thanks! I got it!

    $$25/3$$
     
  5. Dec 1, 2013 #4

    Simon Bridge

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    Well done - don't forget your units.
     
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