# Special relativity (length contraction, velocity composition) problem

• greg_rack

#### greg_rack

Gold Member
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)?

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