Lorentz transformation, special relativity problem

[mhen333]

Homework Statement

Frame S and S' are moving with respect to each other in the x-axis with some velocity. An event happens in S' at x'_1 = 1.0 c*year at t'_1 = 1.0 year. Another event happens at t'_2 = 2.0 c*year at t'_2 = 0.5 year. The two events are simultaneous at some point in S. The origins of S and S' are coincident at time t' = t = 0. Find the relative velocity of the frames, and the time in S when the events are noticed.

Homework Equations

$$t ' = \gamma \left(t - \frac{vx}{c^2}\right)$$
$$x ' = \gamma \left(x - vt \right)$$

The Attempt at a Solution

I really didn't even know where to start. I know that t_1 and t_2 as seen from S are equal, because the events were simultaneous. I tried listing out the equations, but I don't have enough equations for the amount of variables that I need to solve for. The assignment has already been turned in, and I know the answer of V (it was given in the back of the book), but I'd really like to know how to do the problem.

 

[vela]

You have

$$\begin{align*}<br /> t'_1 &= \gamma\left(t_1 - \frac{vx_1}{c^2}\right) \\<br /> t'_2 &= \gamma\left(t_2 - \frac{vx_2}{c^2}\right)<br /> \end{align*}$$

Subtract the first equation from the second. What do you get?

 

[mhen333]

I get the right answer, thanks a ton!

I just need to do a lot more problems until I get comfortable with it, I think.

Thanks again!