In the frame S two electrons approach each other each having

In the frame S, two electrons approach each other, each having a speed v = 0.5c. What is the relative speed of the two electrons? (In other words, what is the speed of one electron as observed in the rest frame of the other electron?)

Solution

Here ,

speed of electrons , u1 = 0.5 c

u2= =0.5 c

Now , for the relative speed of electrons

v = (v1 - v2)/sqrt(1 - v1*v2/c^2)

v = (0.5 c - (-0.5 c))/(1 + 0.5 * 0.5)

v = 0.8 * c

the relative speed of one electron to another is 0.8 * c