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Two spaceships leave Earth in opposite directions, each with a speed of $0.5c$ with respect to Earth. \begin{abcliste} \abc What is the velocity of the first spaceship relativ to the second spaceship? \abc What is the velocity of spaceship two relative to spaceship one? \end{abcliste}
\begin{abcliste} \abc If we name the Earths frame $\mathcal{S}$ and the frame of spaceship two $\mathcal{S'}$, then the relative velocity of the two is $v=0.50c$. The speed of spaceship one in $\mathcal{S}$ is then $v_1=+0.50c$. The speed of spaceship one in $\mathcal{S'}$ is: \begin{align} u' &= \frac{uv_1}{1\frac{v_1u}{c^2}}\\ &= 0.80c \end{align} \abc Since the problem is symmetric, we know that $u''=0.80c$. \end{abcliste}
09:04, 20. June 2017  ssi  Urs Zellweger (urs)  Current Version 
23:13, 3. June 2017  Initial Version.  Urs Zellweger (urs)  Compare with Current 