Draw a clearly labelled “Minkowski spacetime” diagram illustrating two events
((1) a farmer firing his laser gun at his cow, which is sitting along his positive x-direction, and
(2) the cow dying) as observed by two observers (S at rest in the farmer’s and cow’s frame,
and S’ moving at 0.5 c in the direction of the negative x direction.
Show on the diagram, qualitatively, hyperbolae which determine the scale of the ct, x and
ct’, x’ axes. Using the diagram, is there any frame S’ where it appears that the cow dying
caused the farmer to shoot his gun?
See attached file for my diagram so far
The Attempt at a Solution
on my diagram you can see the S and S' frames, where S' is moving in the negative x direction with a velocity of 0.5c. I'm aware that the angle between the axes of the two different frames are governed by the velocity of the S' frame. The question asks for hyperbolae which determine the scale, i'm not sure where these should go. The black dot shows the farmer firing the gun and the red dot show the time when the cow dies in each frame, should the hyperbola pass through both of these points?