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Arc Length curve

  1. Oct 21, 2007 #1
    1. The problem statement, all variables and given/known data

    Find the point on the curve r(t) = (5Sint)i + (5Cost)j + 12tk
    at a distance 26pi units along the curve from the point (0,5,0) in the direction of increasing arc length.

    2. Relevant equations

    L = int (|v|) from 0 to T.

    3. The attempt at a solution

    T comes to be 2pi and when substituted, the position comes to be (0,5,24pi). However, this calculation and answer though correct (according to the back of the book) does not involve the use of the fact that at time t=0, the particle is at (0,5,0).

    What for is that information given then?
     
  2. jcsd
  3. Oct 21, 2007 #2

    arildno

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    It certainly uses that info, in a rather subtle way; namely indirectly telling you that the initial value of t should be zero.

    Thus, if s is the arclength parameter, we have the relationship t=s/13.
     
  4. Oct 21, 2007 #3
    Thanks!!

    Thanks a ton!! I never knew that!
     
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