Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2013 / Paper 1 / Section B / B8 / a / 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 $u$:The required launch components are $u_x=v=3c/5$ and $u_y=\sqrt{u^2-v^2}=\sqrt{7}c/5$.