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

To find the relative velocity of two particles moving towards each other at relativistic speeds, we use the relativistic velocity addition formula: $ v_{rel} = \frac{v_1 + v_2}{1 + \frac{v_1 v_2}{c^2}} $. Substituting $ v_1 = 0.741c $ and $ v_2 = 0.543c $, we get $ v_{rel} = \frac{0.741c + 0.543c}{1 + \frac{0.741 \times 0.543}{c^2}} = 0.916c $.

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