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Relativistic Mechanics

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.

Reveal Answer
v′=(vx−V)2+vy2(1−V2/c2)1−vxV/c2v^{\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}}
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