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Need help with Lorentz Transformation equations

  1. May 11, 2005 #1
    A red light flashes at position xr = 3.00 m and time tr = 1.00*10^-9s, and a blue light flashes at xb = 5.00 m and tb = 9.00*10^-9s, all measured in the S reference frame. Reference frame S' has its origin at the same point as S at t = t' = 0; frame S' moves uniformly to the right. Both flashes are observed to occur at the same place in S'. (a) Find the relative speed between S and S'. (b) Find the location of the two flashes in frame S'. (c) At what time does the red flash occur in the S' frame?

    I don't understand how to start part a. Any help would be great! thx!
     
  2. jcsd
  3. May 12, 2005 #2

    jtbell

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    Staff: Mentor

    You have two events, so you have two pairs of Lorentz transformation equations:

    [tex]x'_r = \gamma (x_r - v t_r)[/tex]
    [tex]t'_r = \gamma \left(t_r - \frac{v x_r}{c^2}\right)[/tex]

    [tex]x'_b = \gamma (x_b - v t_b)[/tex]
    [tex]t'_b = \gamma \left(t_b - \frac{v x_r}{c^2}\right)[/tex]

    where [itex]\gamma = \frac {1} {\sqrt{1 - v^2 / c^2}}[/itex]

    You're given the unprimed x's and t's. You're given that [itex]x'_r = x'_b[/itex], so you can replace [itex]x'_r[/itex] with [itex]x'_b[/itex] in the equations above, or you can do it the other way around if you like.

    Now, how many unknowns do you have, and how many equations? :wink:
     
  4. May 12, 2005 #3
    where in the text am I given that xr = xb?

    EDIT: I found where it says xr = xb in the text. It says "Both flashes are observed to occur at the same place in S'." I just missed that...
     
    Last edited: May 12, 2005
  5. May 12, 2005 #4
    Reference frame S' has its origin at the same point as S at t = t' = 0; frame S' moves uniformly to the right. Both flashes are observed to occur at the same place in S'.
     
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