Lorentz transformation for simultaneous events in different frames

[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!

 

[jtbell]

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!

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?

 

[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...

 

[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'.