A relativistic particle with charge \(Q\) and mass \(M\) moves in the presence of a uniform electric field \(\mathbf{E}=E_{0} \hat{\boldsymbol{z}}\). The initial energy is \(K_{0}\) and the momentum is \(p_{0}\) in the \(\hat{\boldsymbol{y}}\) direction. Show that the trajectory in the \(y\)-z plane is described by

\[z=\frac{K_{0}+M c^{2}}{Q E_{0}} \cosh \left(\frac{Q E_{0}}{p_{0} c} y\right) .\]