Answer
See explanation.
Work Step by Step
a. Let your (the starfighter) frame be S and the enemy be S’.
Let the positive direction be the direction in which S’ travels.
The velocity of the missile relative to the enemy is v’ = 0.700c. The velocity of the enemy relative to you is u=0.400c. Use the relativistic velocity addition formula, equation 37.23.
We are looking for v, the velocity of the missile relative to you.
$$v_x=\frac{v_x’+u}{1+\frac{uv_x’}{c^2}}$$
$$v_x=\frac{0.700c+0.400c}{1+(0.400) (0.700) }=0.859c$$
b. $t=\frac{L}{v}=\frac{8.00\times10^9m}{(0.859)(3.00\times10^8m/s)}=31.0s$
