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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+0.5c}{1+\frac{0.5c \cdot 0.5c}{c^2}}\\ &= 0.80c \end{align}
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