1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook