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Writing equations for rate of change problems

  1. Dec 12, 2009 #1
    Im trying to write an equation for the question below. i did write one but am pretty sure it is wrong because I need to differentiate arctan in it and we have not been taught that yet. Could someone please point me in the right direction with writing it?

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

    A telescope is 75m above water level on a cliff and a boat is approaching at 6m/s. what is the rate of change of angle of the telescope when the boat is 75m from shore.

    2. Relevant equations

    3. The attempt at a solution

    I thought it might be y=arctan(75/x) because the angle specified is found using arctan(opposite/addjacent).

    Any suggestions appreciated :)
  2. jcsd
  3. Dec 12, 2009 #2


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    Hi Poppynz! :smile:

    Just write it tanθ = 75/x, and differentiate both sides wrt x

    from the chain rule, you'll get a sec2θ, which you can rewrite in terms of the original 75/x :wink:
  4. Dec 12, 2009 #3
    Thanks that seems much easier :)
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