Special Relativity question - SHOULD be easy

[joker_900]

Homework Statement

The space and time coordinates of two events as measured in a frame S are as follows:

Event 1: x1 = x0, t1=x0/c
Event 2: x2 = 2x0, t2=x0/2c

Show that there exists an inertial frame in which these events occur at the same time, and find the velocity of this frame relative to S.

Homework Equations

Lorentz Transformations

dx = k(dx' + vdt') and dt = k(dt' + vdx'/c^2)

(I'm writing delta as d and gamma as k as I can't do the symbols here)

The Attempt at a Solution

Now I'm pretty sure that the v is the velocity of frame S' relative to S?

So I used these equations, and made the second one

c^2dt/v = k(c^2dt'/v + x')

Subtracting the first equation from this gives:

c^2dt/v - dx = kc^2dt'/v + kdx' - kdx' - kvdt'


But if the two events are simultaneous in S', then dt'=0.

so c/2v = 1

v/c = 0.5
beta = 0.5


Unfortunately the answer is -0.5, which is important later in the question, and I cannot work out why. I'm sure the equations are right, and surely the v in that is the velocity of S' relative to S, which is what I'm after here?



Thanks!

 

[learningphysics]

Please show exactly how you got from:

c^2dt/v - dx = kc^2dt'/v + kdx' - kdx' - kvdt'

to:

so c/2v = 1

you're making a mistake with signs or something here... in this step.