Problem 3.377

At the moment $t=0$ a relativistic proton flies with a velocity $\mathbf{v}_ {0}$ into the region where there is a uniform transverse electric field of strength $\mathrm{E}$, with $\mathbf{v}_ {0} \perp \mathbf{E}$. Find the time dependence of (a) the angle $\theta$ between the proton's velocity vector $\mathbf{v}$ and the initial direction of its motion; (b) the projection $v_{x}$ of the vector $\mathbf{v}$ on the initial direction of motion.