Special relativity (length contraction, velocity composition) problem

AI Thread Summary
The discussion revolves around a special relativity problem involving length contraction and velocity composition. The calculated velocity of an object relative to Earth is 0.34c, using the formula for velocity transformation. The key issue raised is whether the length measured by the crew, who are in motion with the object, should be considered a proper length or a contracted length. It is noted that the crew is relatively static with respect to the object before it is thrown, complicating the interpretation of the measurements. The conversation highlights the challenges and confusions often encountered when applying the principles of relativity.
greg_rack
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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)?
 
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The crew is pretty static wrt the object :smile: -- before they throw it, that is :wink: !

##\ ##
 
BvU said:
The crew is pretty static wrt the object :smile: -- before they throw it, that is :wink: !

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