Two electrons move in opposite directions at 0.70c as measured in the laboratory. The speed of one electron as measured from the other is:
A) 0.35c
B) 0.70c
C) 0.94c
D) 1.00c
E) 1.40c

Question

Quizplus · Accepted Answer

To find the relative speed of one electron as observed from the other, we use the formula for relativistic velocity addition: $v_{rel} = \frac{v_1 + v_2}{1 + \frac{v_1 \cdot v_2}{c^2}}$, where $v_1$ and $v_2$ are the velocities of the two electrons (0.70c and -0.70c, respectively, since they move in opposite directions), and $c$ is the speed of light. Plugging in the values, we get $v_{rel} = \frac{0.70c - 0.70c}{1 - 0.49} = \frac{0}{0.51} = 0$, which seems incorrect due to a mistake in calculation. The correct calculation should be $v_{rel} = \frac{0.70c + 0.70c}{1 + \frac{(0.70c) \cdot (0.70c)}{c^2}} = \frac{1.40c}{1 + 0.49} = \frac{1.40c}{1.49} \approx 0.94c$, which gives the correct answer as approximately 0.94c.

Two Electrons Move in Opposite Directions at 0