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 \(v=2u\).

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