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Homework Help: Time Dilation question

  1. Feb 1, 2009 #1
    Question:

    The record for the fastest speed at which anyone has ever traveled, relative to the Earth, is held by the Apollo X modue at 24,791 mi/h on their return trip from the moon.
    At this speed, what is the percent difference between the clocks on the Apollo and the clocks on Earth?

    OK, I think I understand how to do the problem, but I'm not getting the answer that our text gives.

    I set the moving IRF as the Apollo and the stationary frame as the Earth.
    I then found the time elapsed in the frame of the spaceship by using d=vt and the given velocity and the distance from the earth to the moon.
    So:

    VApollo=V=24,791mi/h=11082.3m/s
    d(Earth to Moon)=3.84x10^8 m

    With no time dilation for the ship, the time elapsed then is:
    from d=vt: tApollo=t'=3.84x10^8 m/11082.3m/s = 34649.85 s

    I then found the time dilation for the time elapsed in Earth's reference frame using Lorentz tranformation:
    t=t'/[tex]\sqrt{1-(V/c)^2}[/tex]

    gives an elapsed time in Earth' IRF of 346449.85s

    and 346449.85s/34649.85s = 9.985%

    The correct answer is 6.82x10^-8 s

    Could someone help me figure out where I went wrong? I went over the math a few times, so it must be my logic...

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



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 1, 2009 #2

    Delphi51

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    Homework Helper

    I don't have a calculator handy, but something went wrong in that square root calc. Did you note that the spacecraft speed is in mph, so in the same units c = 186000*3600 ?

    Doubtless that square root is well within 1% of 1.
     
  4. Feb 1, 2009 #3
    Yeah, I actually converted the velocity to m/s I just skipped the conversion work.
     
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