Need help with Lorentz Transformation equations

1. May 11, 2005

andrew410

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. May 12, 2005

Staff: Mentor

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

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

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

where $\gamma = \frac {1} {\sqrt{1 - v^2 / c^2}}$

You're given the unprimed x's and t's. You're given that $x'_r = x'_b$, so you can replace $x'_r$ with $x'_b$ 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?

3. May 12, 2005

andrew410

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
4. May 12, 2005

whozum

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'.