# Special relativity velocity and spaceships!

## Homework Statement

---------> A. B <----------
v. v
------------------------------------ this is static frame of ref (D) the space station

Where v=0.97c

In the static frame of reference, ship A has the same length as ship B and are travelling towards eachother. Calculate the speed of ship A relative to ship B according to an observer on the space station. Express your answer as a multiple of vA.

Use your answer as part of a short argument to show that the time required for the whole of ship A to pass through the whole of ship B is ΔtA, as observed from the space station.

## Homework Equations

v'= u - v / 1-vu/c^2

## The Attempt at a Solution

I think that v' = 0.97c - (-0.97c) / 1 - 0.97c*-0.97c/c^2 because they are travelling towards eachother and comes out approximately as 2.9995e8 ms^-1... Or am I barking up the wrong tree and how would you express as a multiple of vA?

How would I work out the 2nd part though... I'm stumped?

Help much appreciated... Thanks for reading