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Homework Help: Special relativity and velocity of a particle

  1. Feb 20, 2005 #1
    hi, im having a little trouble figuring this problem out.

    Two particles in a high-energy accelerator experiment are approaching each other head-on. Each has a speed which is f times the speed of light, as measured in the laboratory. What is the magnitude of the velocity of one particle relative to the other? Give your answer as a fraction of the speed of light.

    I belive that you will have to use the lorentz velocity transformation equation which is v_1= v_2+u/(1+u*v_2/c^2) . but the answer doesnt involve u so im not sure where to go with this problem.

  2. jcsd
  3. Feb 20, 2005 #2

    Andrew Mason

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    The velocity of the one particle relative to the other is:

    [tex]u = \frac{v_1 - v_2}{1 - v_1v_2/c^2}[/tex]

    Where v_2 = - v_1 = fc, you get:

    [tex]u = 2fc/ (1 + f^2)[/tex]

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