Answer
a. 0.882c.
b. -0.882c.
As expected, the relative velocity in part a is the negative of the relative velocity in part b.
Work Step by Step
a. Reference frame S is the second spaceship and reference frame is the Earth.
Let the direction of the first spaceship be the positive direction. We see that v = 0.60c because this is the velocity of Earth relative to the second spaceship.
The velocity of the first spaceship relative to the Earth is given as u’=0.60c. Use equation 26–10 to solve for the velocity of the first spaceship relative to the second spaceship.
$$u=\frac{v+u’}{(1+\frac{vu’}{c^2})}=\frac{0.60c+0.60c}{1+(0.60)(0.60)}=0.882c$$
b. Reference frame S is the first spaceship and reference frame is the Earth.
Let the direction of the first spaceship be the positive direction. We see that v = -0.60c because this is the velocity of Earth relative to the first spaceship.
The velocity of the second spaceship relative to the Earth is given as u’=-0.60c. Use equation 26–10 to solve for the velocity of the second spaceship relative to the first spaceship.
$$u=\frac{v+u’}{(1+\frac{vu’}{c^2})}=\frac{-0.60c-0.60c}{1+(-0.60)(-0.60)}=-0.882c$$
As expected, the relative velocity in part a is the negative of the relative velocity in part b.