Solution
= Solution
Put the station at $(0,0)$ and take B's initial position to be $(0,a)$. Interception after time $t$ requires A to cover displacement $(vt,a)$ at <speed> $u$:
$$
u^2t^2=v^2t^2+a^2,\qquad
\boxed{t_{\rm out}=\frac{a}{\sqrt{u^2-v^2}}=\frac{5a}{\sqrt7c}=1.890\,\mathrm{days}.}
$$
The required launch components are $u_x=v=3c/5$ and $u_y=\sqrt{u^2-v^2}=\sqrt7c/5$.