(A2-9) Cormorant wonders just how fast he and his cousin will have to go as they approach one another, so that their relative velocity will exceed light speed.
Starting again with the velocity transformation, the combined velocities of the seabirds is given by Shag's velocity in Cormorant's frame of reference:
First, let’s simplify things by expressing all the velocities (wN, wC, u and c) as fractions of the speed of light. So, for example, if Shag flies at 60% of the speed of light, his velocity is just 0.6, while light speed itself is 1. Then, recalling that in Cormorant's setup, he and Shag fly towards one another with equal but opposite velocities (relative to Nefertiti), we can simply things further by recognising that wN = -u.
① Rewrite the velocity transformation equation in terms of wN using these simplifications
Now, Cormorant's question is how fast he and his cousin need to be moving for their combined velocities, given by wC, to equal the speed of light (= 1 using our velocity units).
② Set the expression equal to 1, rearrange and solve to find the individual speeds the birds would need to achieve.
