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An astronaut in a rocket traveling at $0.5c$ (with respect to Earth) observes a meteor come from behind and passing him at a speed he measures to be $0.5c$. How fast is the meteor moving with respect to earth?
The speed of the meteor in the $\mathcal{S'}$ frame is $0.5c$. The speed in the Earth frame is therefore: \begin{align} u &= \frac{u'+v}{1+\frac{vu'}{c^2}}\\ &= \frac{0.5c+.5c}{1+\frac{.5c \cdot .5c}{c^2}}\\ &= 0.80c \end{align}
08:55, 20. June 2017  si  Urs Zellweger (urs)  Current Version 
23:10, 3. June 2017  Initial Version.  Urs Zellweger (urs)  Compare with Current 