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Homework Help: Circular motion word problem

  1. Mar 27, 2013 #1
    1. The problem statement, all variables and given/known data
    A lighthouse is located on a small island 3km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute. How fast is the beam moving along the shoreline when it is 1km from P?

    2. Relevant equations

    3. The attempt at a solution

    I drew a picture and got a triangle out of it. I labeled the center angle θ and a straight line from P that's 1km long as X.

    Tan θ = x/3

    Want dx/dt when dθ/dt = 24∏

    The reasoning was that
    C = 2∏r


    C=6∏ but 4 revolutions/min gives me 24∏.

    I get dx/dt = 80∏ as the solution, that seems way too fast.
  2. jcsd
  3. Mar 27, 2013 #2


    User Avatar

    Staff: Mentor

    4 revolutions per minute gives 2∏ radians per 15 seconds. What does that give you for ω in units of radians per second?
  4. Mar 28, 2013 #3
    Hmm I'm not following... Could you tell me how you arrived at that?
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