Two particles in a high-energy accelerator experiment are approaching each other head-on, each with a speed of 0.9520c as measured in the laboratory. What is the magnitudeof the velocity of one particle relative to the other

the magnitude of the velocity of one particle relative to the other is 0.9988c

Explanation:

Given the data in the question;

Velocities of the two particles = 0.9520c

Using Lorentz transformation

Let relative velocity be W, so

v = ( u + v ) / ( 1 + ( uv / c²) )

since each particle travels with the same speed,

u = v

so

v = ( u + u ) / ( 1 + ( u×u / c²) )  

v = 2(0.9520c) / ( 1 + ( 0.9520c )² / c²) )  

we substitute

v = 1.904c / ( 1 + ( (0.906304 × c² ) / c²) )  

v = 1.904c / ( 1 + 0.906304 )

v = 1.904c / 1.906304

v = 0.9988c

Therefore, the magnitude of the velocity of one particle relative to the other is 0.9988c