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An observer on Earth sees an alien vessel approach at a speed of $0.6c$. The \emph{Hunter spaceship} comes to the rescue, overtaking the aliens while moving directly toward Earth at a speed of $0.9c$ relative to Earth. What is the relative speed of one vessel as seen by the other?
The relative speed of the two vessels as seen on Earth is of course $0.90c0.60c=0.30c$.\\ In the reference frame of the alien vessel, the Earth is moving at $0.60c$ (i.e. towards the alien vessel) and the \emph{Hunter} vessel is moving $+0.90c$ relative to the Earth. Thus the speed of the \emph{Hunter} as seen from the alien vessel is \begin{align} u &= \frac{v+u'}{1+\frac{vu'}{c^2}}\\ &= \frac{0.6c+0.9c}{1+(0.6)(0.9)}\\ &= 0.65c \end{align}
19:54, 3. Sept. 2017  solution  Urs Zellweger (urs)  Current Version 
23:15, 3. June 2017  Initial Version.  Urs Zellweger (urs)  Compare with Current 