Pursuit and chase

Point A moves uniformly with velocity v that is continually "aimed" at point B which in turn moves rectilinearly and uniformly with velocity $u<v$ . At the initial moment of time $v$ is perpendicular to $u$ and the points are separated by a distance $L$ .

If at some instant their velocities make certain angle (say $x$ ) and by that time the distance traversed by A perpendicular to the motion of B is $\dfrac L4$ , find the value of the angle $x$ if $v=2u$ .