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Homework Help: Using rapidity - prove velocity transformation equations

  1. Jul 10, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove the law of transformation of velocities

    {v_x} = \frac{{{v_x}^\prime + V}}{{1 + {v_x}^\prime V/{c^2}}}\\
    {v_y} = \frac{{{v_y}^\prime }}{{\gamma (1 + {v_x}^\prime V/{c^2})}}\\
    {v_z} = \frac{{{v_z}^\prime }}{{\gamma (1 + {v_x}^\prime V/{c^2})}}

    2. Relevant equations

    Rapidity equations

    3. The attempt at a solution
    I proved Vx with an ease using rapidity equations and the identity for tanh(a+b)
    now, I'm stuck with revealing the relation to Vy and Vz.
  2. jcsd
  3. Jul 10, 2011 #2
    What happens if you use the same method you used to prove the first equation, except taking into account that a distance in some direction orthogonal to V is the same in both coordinate systems?
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