How to Calculate Positions of Observers Using Lorentz Transformation

[mrjeffy321]

I cannot seem to figure out how to do this problem.

The situation is,
There are two events occurring a given time apart at the same location as seem by an observe in one frame (S). Another observer (S') sees these two events occurring at a differnent amount of time apart. I am trying to find the difference in posisitons of the two observers.

I know that,
x' = (x - ut) / sqrt(1 - u^2/c^2) = gamma*(x - ut)
t' = (t - ux/c^2) / sqrt(1 - u^2/c^2) = gamma*(t - ux/c^2)

But these two equations have too many unknowns for me. All I know are the two times for each observer and the fact that the events occur at the same spot. If I do not know the speed of the S' observer, how can I figure this out?

 

[Galileo]

You have to assume u is known ofcourse, since the answer depends on the speed of S' relative to S.

 

[mrjeffy321]

I am not given any value for u, only that the S' frame is moving relative the S.
It is not as if I can just assume a value for u, how can I get around this.

 

[mrjeffy321]

it must have something to do with the difference in time the events were seen...of course, since those were to only real numbers given to me (those and the speed of light).


[Only 3 hours left to figure this problem out].