Special Relativity simultaniety

[PhysicsInNJ]

Homework Statement

Two events occur in an inertial system K as follows.
Event 1: x1 = a, t1 = 2a/c, y1 = 0, z1 = 0
Event 2: x2 = 2.6a, t2 = 1.9a/c, y2 = 0, z2 = 0

What is the velocity of the frame K' in which these events appear to occur at the same time? Express the velocity vector using the variables a and c and the unit vectors, i, j, and k; for example, 2*i + 2*j is a vector which bisects the x and y axes.

Homework Equations

Lorentz equations

The Attempt at a Solution

First I assumed that I could use the time dilation, T0=T/Ɣ with T (the observed time) being zero but that obviously will not work. I likewise tried it with length contraction.

I don't know where else to go from here.

 

[Simon Bridge]

HInt: "simultaniety" and "Lorentz transformation".

 

[PhysicsInNJ]

So the K' would have to travel the distance between event 1 and 2, in the amount of time between the events?

 

[TSny]

So the K' would have to travel the distance between event 1 and 2, in the amount of time between the events?

Wouldn't this make the two events occur at the same place in K' rather than occur at the same time in K'?

 

[Simon Bridge]

You know the space-time coordinates for the events in K.
Use the Lorentz transformation to get equations for the space-time coordinates in another reference frame.

 

[Chestermiller]

PhysicsInNJ: Please write down for us the Lorentz equations for $\Delta x'$ and $\Delta t'$ in terms of $\Delta x$ and $\Delta t$.