Answer
0.962 c
Work Step by Step
Let the positive direction be the direction of the second pod, so the answer will be positive. Let the first pod’s reference frame be S and the spacecraft’s reference frame be S’.
The velocity of the spacecraft relative to the first pod is v = +0.70c. The velocity of the second pod relative to the spacecraft is u’=+0.80c.
Use the relativistic velocity addition formula, equation 26–10, to find the velocity of the second pod as measured by the first pod.
$$u=\frac{v+u’}{1+\frac{vu’}{c^2}}$$
$$u=\frac{0.70c+0.80c}{1+(0.70)(0.80)}=0.962c$$
