A charged particle is projected with velocity $ \upsilon_0$ along the positive $x$ - axis. The magnetic field $B$ is directed along negative $z$ - axis for the region $0<x<L$. The particle emerges out at $x = L$ at an angle of $60^{\circ}$ with the direction of projection. Find the velocity with which the same particle is projected at $x=0$ along the $+ve\: x$ - axis so that when it emerges out at $x = L$, the angle made by it is $30^{\circ}$ direction of projection with the
