Calculating the Orientation of a Moving Rod Using Lorentz Transformations

[TheLawR]

1. Problem

Horizontal rod of length x traveling along the positive y-direction at velocity u. Determine the orientation of the rod in frame S', which is moving at velocity v in positive x-direction.


2. Homework Equations

Lorentz Transformation for length contraction, x' = $$\gamma$$(x-Vt)


3. The Attempt at a Solution

I have absolutely no idea how to approach this problem. I have a basic understanding of relativity, and how the transformations work, and I know that the rod will appear slanted, but I am not sure how to calculate in which direction.

Any help understanding this concept is greatly appreciated.

 

[vela]

Try writing down the equations for the world lines of the endpoints of the rod in the unprimed frame. Then use the Lorentz transformation to find the world lines in the primed frame.

 

[TheLawR]

I was able to figure out how it would look like, and how it would be oriented. But we were offered extra credit for doing the algebra. I can't figure out how to work the algebra, or where to start.