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## Homework Statement

Two spaceships, each of length 100m in their rest frames, pass each other travelling in opposite directions. Instruments on ship A find that the front end of B requires a time [tex]5x10^{-6}[/tex]s to transverse the full length of A.

What is the relative velocity of the spaceships?

A clock in the front end of B records 1am as it passes the front end of A. What will it read when it passes the rear end?

## Homework Equations

[tex]\Delta x\prime = \gamma (\Delta x - v\Delta t)[/tex]

## The Attempt at a Solution

I assumed that spaceship A was the stationary frame.

As a result I said that [tex]\Delta x[/tex] = 100m, and [tex]\Delta t[/tex] = [tex]5x10^{-6}[/tex]s.

I then said that [tex]\Delta x\prime = \gamma \Delta x[/tex]. With this information I put it back into the equation given above, and ended up with v = 0. Which I would assume is quite clearly wrong for the question, or it wouldn't have been given to me.

So some questions I have about this, where I'm confused. I assumed that [tex]\Delta x[/tex] and [tex]\Delta x\prime[/tex] have different values, as I assumed that [tex]\Delta x\prime[/tex] would be affected by length contraction of some form or the other. However because it says in that the two lengths are equal in their own rest frame, does that make both [tex]\Delta x[/tex] and [tex]\Delta x\prime[/tex] equal for the question? I think as I went about it, I had too many variables and not enough enquations.