Relativistic Trains in Two Dimensions

[soggybomb]

Homework Statement

A and B are trains on perpendicular tracks, radiating from the origin of a coordinate system S. Train A is moving along the positive Y axis at a velocity of 0.8c, and train B is moving along the positive X axis also at a velocity of 0.8c. All velocites are measures with respect to S.
a) Find the velocity of A with respect to B
b) Find the velocity of B with respect to A
c) Comment on the fact that these two velocities do not point in opposite directions.

Homework Equations

The Attempt at a Solution

I started by transforming the x and y velocities into the A frame and ended up with a vector with a magnitude that was too small. I do know the answers since they are in the back of my book, but I am looking more for methods than a numerical answer.

 

[_coyote_]

Any help would be greatly appreciated!a) The velocity of A with respect to B is the vector (0.8c, -0.6c), since the equation for transforming velocities from one frame to another is: $V_2 = V_{2A} + V_{1A}$b) The velocity of B with respect to A is the vector (-0.6c, 0.8c), since the equation for transforming velocities from one frame to another is: $V_1 = V_{2A} - V_{1A}$c) The fact that these two velocities do not point in opposite directions is due to the fact that the two frames are not moving at the same speed and direction relative to each other.