# Relative length and velocities using Lorentz transformations

• clayton26
In summary, two space ships, A and B, with proper lengths of 100m each, pass each other in opposite directions. According to the clocks on ship A, it takes 1.5 x 10^(-6) s for the front end of B to pass the entire length of ship A. The problem is asking for the relative velocity of the two ships, as well as the time it takes for the front end of A to pass the entire length of ship B according to the clocks on ship B. Additionally, it questions whether the time interval between the front end of A passing the front end of B and the rear end of A passing the front end of B agrees with the answer to the previous question. The Lore

## Homework Statement

Space ships A and B, each having a proper length of 100m, pass each other moving in opposite directions. According to the clocks on ship A, the front end of B takes 1.5 x 10^(-6) s to pass the entire length of A.

a) what is the relative velocity of the two ships?

b) according to clocks on ship B, how long does it take for the front end of A to pass the entire length of ship B?

c) according to clocks on ship B, how much time passes between the time when the front end of A passes the front end of B and the time when the rear end of A passes the front end of B? Does this time interval agree with your answer to B? Should it?

## Homework Equations

Lorentz matrices.

ATTEMPTS:

So here's what's confusing me: I want to apply the lorentz transformation of velocity addition to find the relative velocity of the spaceships, however I'm not sure how to do that since I don't know their respective velocities to begin with. Is there some way to derive the velocity of one or both of the ships given the time it takes for the front end of ship A to pass through the length of ship B? I wanted to simply take delta(x)/delta(t), but I don't know what to use for delta(x) since the problem only gives me the proper length and no velocity to apply a lorentz contraction. So any help with any part of this problem would be greatly appreciated!

What's the length of ship A in ship A's frame? That's the distance the front end of B travels in the 1.5 μs.