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Homework Help: Find the velocity using special relativity

  1. Apr 4, 2008 #1
    [SOLVED] Find the velocity using special relativity

    According to observations on the Earth, the nearest star to the solar system is 4.25 light years away.
    A space ship which leaves the Earth and travels at uniform velocity takes 4.25 years, according to the ship-borne clocks, to reach the star.
    What is the speed of the space ship, expressed as a fraction of the speed of light c?

    Ux = (U'x + v)/(1 + v*U'x/c^2)
    We know that: x = 4.25 light years
    t' = 4.25 years
    c = constant.

    I have been stuck on this question for nearly a week, and i was hoping someone could give me a push in the right direction. Now i know about time dilation and length contraction and that they will be seen differently between the two frames. Thats why i don't suggest that the v of the ship is equal to c.
    I have also tried to rearrange the equation using Lorentz transformations, however in most cases i need gamma which means i need v.
    Any suggestions would be a great help, Thanks.
  2. jcsd
  3. Apr 4, 2008 #2


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    Pick one frame to work from. The simplest is earth. The time in this frame that the ship takes is 4.5*v/c years, yes? Now put the the gamma factor (leaving v as unknown) to get the elapsed ship time. Set it equal to 4.5 years and solve for v.
  4. Apr 4, 2008 #3
    Thank you for the help, i now see how it works and i am able to solve v.
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