Problem 1.358

The velocity components of a particle moving in the $x y$ plane of the reference frame $K$ are equal to $v_{x}$ and $v_{y} .$ Find the velocity $v^{\prime}$ of this particle in the frame $K^{\prime}$ which moves with the velocity $V$ relative to the frame $K$ in the positive direction of its $x$ axis.

v^{\prime}=\frac{\sqrt{\left(v_{x}-V\right)^{2}+v_{y}^{2}\left(1-V^{2} / c^{2}\right)}}{1-v_{x} V / c^{2}}

Relativistic Mechanics