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Homework Help: D/dt |r(t)| = (1/|r(t)|) r(t)dot r'(t)

  1. Sep 20, 2009 #1
    1. The problem statement, all variables and given/known data
    If vector r(t) is not 0, show that d/dt |r(t)| = (1/|r(t)|) r(t)dot r'(t).

    The last part is the dot product of r(t) and r'(t).

    2. Relevant equations

    The hint given was that |r(t)|^2 = r(t) dot r(t)

    3. The attempt at a solution

    Not sure where to begin, but I thought that |r(t)| is the length or magnitude of the vector r(t), thus its derivative is zero. If this is correct, then I also need to prove that the right side = zero.
  2. jcsd
  3. Sep 20, 2009 #2


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    Depending on what r(t) is, surely it's magnitude can change over time?

    Can you take the derivative of both sides of the equation in the hint using the chain rule?
  4. Sep 20, 2009 #3
    Thanks for the hint on the hint. So simple and I didn't see it before.
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