Question

consider 3 inertial frame of reference p , q, r , the frame q moves with velocity c/2 with respect to p and r moves with velocity c/10 with respect to q in the same direction. the velocity of r is measured in p will be

Answer 1

Let's denote $u_2=c/2$ - velocity of q with respect to p, $u_1=c/10$ - velocity of r with respect to q.

To find the velocity of r measure in p, we need to use relativistic formula for velocity addition:

$u_3 = \frac{u_1+u_2}{1+\frac{u_iu_2}{c^2}} = \frac{c/2+c/10}{1+1/20}= \frac{3c}{5} \cdot\frac{20}{21} = \frac{60c}{105} = 0.57c$