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Relativistic Mechanics

Problem 1.363

A particle moves in the frame \(K\) with a velocity \(v\) at an angle \(\theta\) to the \(x\) axis. Find the corresponding angle in the frame \(K^{\prime}\) moving with a velocity \(V\) relative to the frame \(\bar{K}\) in the positive direction of its \(x\) axis, if the \(x\) and \(x^{\prime}\) axes of the two frames coincide.

Reveal Answer
tan⁡θ′=1−β2sin⁡θcos⁡θ−V/c, where β=V/c\tan \theta^{\prime}=\frac{\sqrt{1-\beta^{2}} \sin \theta}{\cos \theta-V / c}, \text { where } \beta=V / c
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