Special relativity - two flashes at different places

[wumple]

Homework Statement

An observer S sees a flash of red light 1200m from his position and a flash of blue light 720 m closer to him and on the same straight line. He measures the time interval between the occurrence of the flashes to be 5.0 microseconds, the red flash occurring first.
(a)What is the relative velocity v of a second observer S' who would record these flashes as occurring at the same place?

Homework Equations

x' = gamma (x - beta W) , W = ct

The Attempt at a Solution

I used the above equation and set delta x' = 0 but I came up with beta = -.32. The back says beta = .48. What did I do wrong?? Thanks in advance!

 

[malawi_glenn]

What did I do wrong??

Very hard to tell because you basically showed no work.

$\Delta x' = \gamma (\Delta x - v \Delta t)$

Now $\Delta x' = 0$ - what does this tell you about $\Delta x - v \Delta t$?
What $\Delta x$ and $\Delta t$ values should be used?

 

[jbriggs444]

Homework Statement

An observer S sees a flash of red light 1200m from his position and a flash of blue light 720 m closer to him and on the same straight line. He measures the time interval between the occurrence of the flashes to be 5.0 microseconds, the red flash occurring first.
(a)What is the relative velocity v of a second observer S' who would record these flashes as occurring at the same place?

Homework Equations

x' = gamma (x - beta W) , W = ct

The Attempt at a Solution

I used the above equation and set delta x' = 0 but I came up with beta = -.32. The back says beta = .48. What did I do wrong?? Thanks in advance!

When in doubt (and when you can), write down coordinates for the events of interest.

In frame S, can you find $(x_r, t_r)$ coordinates for the event where the flash of red light was emitted?
In frame S, can you find $(x_b, t_b)$ coordinates for the event where the flash of blue light was emitted?

In doing this, feel free to define a zero time for your coordinate system as you see fit.

With these coordinates in hand, can you find the invariant separation between the two events? Is it timelike or spacelike? (Given what S' records, one can see what that answer needs to be).

Since this separation is invariant, what does this say about what delay that observer S' records between the two flashes?

With these results in hand, can you calculate a time dilation factor for the proper time of S' compared to the coordinate time of S?

 

[malawi_glenn]

This is in general a relatively good guide on problem solvning in relativity https://phas.ubc.ca/~mav/p200/lttips.html