# Special Relativity - Velocity transformation problem

## Homework Statement

Two spaceships are moving away from Earth at a speed of 0.8c, with one ship following in the flight path of the other. Their separation along the axis of their motion is maintained at 0.1 light years as measures by the spaceships' instruments. A crew exchange vehicle is launched from the rear spaceship to the front spaceship, travelling at 0.9c relative to Earth. Approximately, how long does the trip take for the crew inside the crew exchange vehicle.

## Homework Equations

Lorentz Velocity Transformations:

u' = $\frac{u-v}{1-\frac{vu}{c^{2}}}$

## The Attempt at a Solution

u' = $\frac{0.9c-0.8c}{1-0.72}$
= 0.357c

and

L' = $\sqrt{1-\frac{v^2}{c^2}}$L$_{0}$
= 0.093 light years

$\frac{0.093}{0.357}$ = 0.26 years, or 95 days.

However, the question is multiple choice, and the options are:

A. 1 year
B. 25 days
C. 1 day
D. 10 days
E. 150 days

Can someone please point out where I might have slipped up. Thankyou!

What did you plug in for $v$ in the length contraction equation?