A particle with mass \(m\) and positive charge \(q\) is launched at time \(t = 0\) with an initial velocity \(\vec{v}_0 = v_0 \hat{i}\) into a region containing uniform, parallel electric and magnetic fields given by \(\vec{E} = E \hat{k}\) and \(\vec{B} = B \hat{k}\), where \(E\) and \(B\) are positive constants. Gravitational effects are negligible. Which of the following correctly describes the projection of the particle's trajectory onto the \(xy\)-plane and its motion along the \(z\)-axis for \(t > 0\)?