91影视

When two particle or a body moves with a velocity which is approaching to speed of light then normal method of finding relative velocity does not work as it exceeds the velocity of body greater than velocity of light.

Therefore relative velocity for two particles moving with velocity approaching to speed of light is given by velocity addition method.

Velocity addition method

According the velocity addition method the velocity of particle in lab frame observed by observer in moving frame is given by

$u_x^{\text{'}}=\frac{u_x-v}{1-{\displaystyle \frac{v{u}_x}{c^2}}}---\left(i\right)$

For the velocity of particle moving in moving frame or relativistic frame observed by observer in rest frame is given by inverse Lorentz transformation of first(i) formula

That is

$u_x=\frac{u_x^{\text{'}}+v}{1+{\displaystyle \frac{v{u}_x^{\text{'}}}{c^2}}}$

Where, $u_x^{\text{'}}$is the velocity of body in $S\text{'}$frame (moving frame), $u_x$is velocity of body in frame S (lab frame) and v is velocity of the moving frame.

Given: The speed of first particle in lab frame is $u_{x1}=0.9520c$

The speed of second particle in lab frame is $u_{x2}=-0.9520c$

The speed of moving frame is same as the speed of first particle.

The relative velocity of second particle with respect to first particle is given by

$u_x=\frac{u_x^{\text{'}}+v}{1+{\displaystyle \frac{v{u}_x^{\text{'}}}{c^2}}}$

Put the values of constants in above equation

$$\begin{gathered} u{\text{'}}_{x2}=\frac{-0.9520c+0.9520c}{1+{\displaystyle \frac{\left(0.9520c\right)\left(0.950c\right)}{c^2}}} \\ u{\text{'}}_{x2}=-0.9988c \end{gathered}$$

Thus, themagnitude of the velocity of one particle relative to the other is 0.9988c .