Special relativity (length contraction, velocity composition) problem

[greg_rack]

Homework Statement

The crew of a spaceship travelling with $V=0.75c$ away from earth, throws an object of length(measured by them) $l=45m$. This object is thrown towards earth with a velocity $v=0.55c$. Calculate the length of the object measured by an earth observer.

Relevant Equations

velocity composition
length contraction

First, I calculated the velocity of the object with regards to earth, which is:
$$v'=\frac{V-v}{1-\frac{vV}{c^2}}=0.34c$$
Now, the problem is solved if I consider the length $l=45m$(so by calculating the $\gamma$ factor with $v'$) to be the proper one... but since it's measured by the crew, which has launched it with $v$, wouldn't it be a contracted length that they've measured as opposed to a proper one(which is that measured by a static observer)?

 

[BvU]

The crew is pretty static wrt the object -- before they throw it, that is !

$\$

 

[greg_rack]

The crew is pretty static wrt the object -- before they throw it, that is !

$\$

God, what a slip!
Relativity is really messing me up