Question

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

Answer 1

Answer:

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$_r$ = ( u + v ) / ( 1 + ( uv / c²) )

since each particle travels with the same speed,

u = v

so

v$_r$ = ( u + u ) / ( 1 + ( u×u / c²) )  

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

we substitute

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

v$_r$ = 1.904c / ( 1 + 0.906304 )

v$_r$ = 1.904c / 1.906304

v$_r$ = 0.9988c

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