Answer
See explanation.
Work Step by Step
a. For the pursuit ship to catch the cruiser, the velocity of the cruiser should be directed toward the pursuit ship.
b. Let the positive direction be the direction in which the pursuit ship S’ travels.
The velocity of the pursuit ship relative to Tatooine is u = 0.800c.
The velocity of the cruiser relative to Tatooine is v=0.600c.
The velocity of the cruiser relative to the pursuit ship is v’. Use the relativistic velocity addition formula, equation 37.23.
$$v_x=\frac{v_x’+u}{1+\frac{uv_x’}{c^2}}$$
$$0.600c=\frac{ v_x’+0.800c}{1+(0.800) (v_x’)/c }$$
$$ v_x’=-0.385c$$
