- #1

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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)?

$$v'=\frac{V-v}{1-\frac{vV}{c^2}}=0.34c$$

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)?