Answer to Question #178527 in Mechanics | Relativity for Samir

Question

 A pion moving with speed 0.6c emits a muon in the same direction. Speed of muon in the rest frame of pion is 

0.4c. calculate the speed of muon in lab frame.

Answer 1

Explanations & Calculations

• Since the speeds described here are relativistic, simple velocity addition cannot be employed to calculate the relative speed instead relativistic addition which is given by the equation $\small V_{relative}=\large\frac{U+v^1}{1+\frac{Uv^1}{C^2}}$ should be used.

• Then, how a person on earth sees the motion of the muon is

$\qquad\qquad \begin{aligned} \small V&=\small \frac{0.6C+0.4C}{1+\large\frac{0.6C\times0.4C}{C^2}}\\ &=\small \frac{1.0C}{1+0.24}\\ &=\small \bold{0.806C} \end{aligned}$