Simple Lorentz transformation problem

[brooktrout]

Homework Statement

3. At what speed (measured in units so c = 1) must the train be moving in order for the points(X,T) = (1,1) and (X,T) = (5,2) to be simultaneous in the (X',T') coordinate system?

Homework Equations

Disclaimer: I'm not actually in a physics class, I'm in an elementary college math class that's doing a special relativity unit. So I know very little about physics.

I do know we have to use Lorentz Transformations, so that would be:

X= X'/(square root (1-(v^2/c^2) + VT'/(square root (1-(v^2/c^2)
and T = VX'/C^2(square root (1-(v^2/c^2) + T'/square root (1-(v^2/c^2)

The Attempt at a Solution

OK, so here's the thing. I just want to know where to begin; i.e., how to set up my equations. I can do the math once I get there, but I really don't even get what this question is asking...where do I put in the given coordinates, and to which of the given equations? That's all I need to know.

Thank you so much! Hope this followed all forum guidelines, I'm not looking for anybody to do my homework at all, just a little hint about where to start.

 

[Doc Al]

You have the equations. (I suggest you write them in terms of Δx, Δx', Δt, and Δt'. See: https://www.physicsforums.com/showpost.php?p=905669&postcount=3")

For the events to be simultaneous in the primed frame, what must be true? Plug that in and solve for v.

 

[tiny-tim]

welcome to pf!

hi brooktrout! fishy welcome to pf!

(have a square-root: √ and try using the X² tag just above the Reply box )

3. At what speed (measured in units so c = 1) must the train be moving in order for the points(X,T) = (1,1) and (X,T) = (5,2) to be simultaneous in the (X',T') coordinate system?

hint: the 4-vector joining them is (4,1)