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Homework Help: Resultant Velocities in 2D (Relativistic)

  1. Oct 4, 2016 #1
    1. The problem statement, all variables and given/known data
    Here's the question:


    2. Relevant equations
    Just the usual Lorentz transform matrix etc.

    3. The attempt at a solution

    Now, the last line is clearly incorrect, since it tends towards infinite relative speed as v --> c. Of course the initial answer of sqrt(2)v for the first part is fine because that isn't relative speed (I am pretty sure I have this part right - let me know if not). I have a feeling I can't 'Pythagorise' the 3-velocity part of Vrel4 to get a magnitude, but this is a bit of a guess. Vrel4 still seems to obey the V.V = (+/-)c^2 inner product identity so that points towards it being the correct 4-vector, although I may be wrong about that.

    Thanks for any help.

    (check the imgur links, pictures didn't work)
    Last edited: Oct 4, 2016
  2. jcsd
  3. Oct 5, 2016 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    I don't know what you did, since you posted all your work in an image and I do not look at those---only at typed solutions. (Most other helpers won't look at it either.) Consult the PF Guidelines.

    However, the way I would approach the problem if I were solving it would be to go into the rest-frame of ejected particle 1, and use Lorentz-transformation equations go get the (vector) velocity of ejected particle 2 in that new frame. From that, the relative speed is easy to get.
    Last edited: Oct 6, 2016
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