In an "atom smasher," two particles collide head on at relativistic speeds. If the velocity of the first particle is 0.741c to the left, and the velocity of the second particle is $0.543 c$ to the right (both as measured in the lab rest frame), how fast are the particles moving with respect to each other?
A) 0.916c
B) 1.284c
C) 0.934c
D) 0.834c

Question

Quizplus · Accepted Answer

The relative velocity of the particles is given by the relativistic velocity-addition formula:$$v_{rel} = \frac{v_1 - v_2}{1 - \frac{v_1 v_2}{c^2}}$$where $v_1$ and $v_2$ are the velocities of the particles as measured in the lab rest frame, and $c$ is the speed of light. Plugging in the given values, we get:$$v_{rel} = \frac{0.741c - 0.543c}{1 - \frac{0.741c \times 0.543c}{c^2}} = 0.916c$$Therefore, the particles are moving with respect to each other at a speed of 0.916c.

In an "Atom Smasher," Two Particles Collide Head on at Relativistic