Question

Two electrons approaches each other with equal speeds 0.9c. Find the speed of one electron w.r.t. the other.

Answer 1

Explanations & Calculations

• Since the speeds are relativistic, only the relativistic velocity addition can be used.
• Using the equation $\small V_{relative}=\large \frac{U+v}{1+\large\frac{U\times v}{C^2}}$ where $\small U$ is the velocity of a frame S, $v$ the velocity of any arbitrary particle relative to the frame S & $\small V$ is the relative velocity of the particle relative to a stationary frame P.
• For the ease stop one frame & put its velocity on the other
• Then the knowns are $\small U=\rightarrow 0.9C$ and $\small v=\rightarrow 0.9C$
• Then,

$\qquad\qquad \begin{aligned} \small V_{relative}&=\small \frac{0.9C+0.9C}{1+\large\frac{0.9C\times0.9C}{C^2}}\\ &=\small \frac{1.8C}{1.81}\\ & =\small\bold{0.9945C} &\small \end{aligned}$

• Each electron sees the other electron approaching with a velocity of 0.9945C