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Vectors and max distance

  1. May 13, 2012 #1
    Hello,

    If I have a vector A and then I do the dot product on itself so A°A. Then can I use that to find the maximum distance from the origin? If I take the derivative of the dot product then can I know at what time the maximum distance was travelled?

    I have done this but it is wrong based on the graph I made using Wolfram Alpha, I just need some reassurance that I'm on the right track.
     
  2. jcsd
  3. May 13, 2012 #2

    tiny-tim

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    hello jimmy42! :smile:

    your method looks ok …

    distance2 = A.A,

    so if the distance is a maximum, then A'.A = 0

    ie A' is perpendicular to A
     
  4. May 22, 2012 #3
    Why if A'.A =0 is the distance a maximum?

    I too have a question on this, and I'm failing to see why if the position vector and the velocity vector are perpendicular then the distance is a maximum if the above holds true.

    Cheers in advance

    Smithy
     
  5. May 22, 2012 #4

    tiny-tim

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    Welcome to PF!

    Hi Smithy! Welcome to PF! :smile:
    Because that's the derivative of the distance squared (divided by 2),

    so it must be 0 if the distance squared is at a turning-point (maximum minimum or inflection point). :wink:
     
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