(2-8)    Here's what happens in the experiment, in Cormorant's frame of reference (frame C).


As Nefertiti, on the ground sees it, in her frame of reference (frame N), Cormorant is flying away to the right, with a velocity u. In Cormorant's frame C, however, he remains stationary at the origin and it is you and Nefertiti who move, to the left, with velocity u.   


Two things happen in Cormorant's frame of reference, while he records a time tC on his stopwatch:  Nefertiti moves away by a distance xC and the light travels a distance r to reach you.


①  Write down an expression for distance xC, in terms of velocity and time.

②  Write down an expression for distance r, in terms of velocity and time.

 

③  Now let's switch to Nefertiti's frame of reference. The distance travelled by the light to reach you, as she sees it, is y, and she records the time taken as tN. Write down an expression for y in terms of velocity and time. 

 

④  Now for the good bit. Notice what type of triangle is formed by the three lengths r, x and y. Prompted by this observation, and with the help of an ancient Greek of your choice, write down the relationship between the three side lengths. Then by rearranging, deduce an expression for tC as a function of tN.