Question

What happens in the relativistic addition of velocities formula (derived in
problem (10) when one of the velocities (say, vBA) is the speed of light??

Answer 1

relativistic addition of velocities formula:

$$v_B = \frac{v_A+v_{BA}}{1+v_A \cdot v_{BA}}$$

If one of the velocities (say, vBA) is the speed of light, $v_{BA}=1$ and

$$v_B = \frac{v_A+1}{1+v_A \cdot 1} = 1$$

Therefore, $v_B = 1$ and does not depend on $v_A$ .