A particle of charge \(Q\) and mass \(M\) starts at the origin of the coordinate system with initial speed \(v_{0}\) in the \(\hat{\boldsymbol{z}}\) direction. There are uniform electric and magnetic fields \(E\) and \(B\) in the \(\hat{\boldsymbol{x}}\) direction. Find the location of the particle when it has reached one half of its maximum value in \(z\) for the first time.