Question

Two space ships race toward a planet. One can go 0.8c, and the other only makes a top speed of 0.6c, but it had a head start. At the moment the faster ship passes, the slow ship launches a beacon which also goes 0.6c (relative to the ship which launched it). The beacon emits a 1THz microwave signal. Assume the ships are so close together that this is essentially a one dimensional problem. [HINT: One answer below is really easy.]
a) Find the speed of the beacon relative to the planet.
b) Find the speed of the beacon relative to the fast ship.
c) What is the speed of the microwave signal relative to the ship and relative to the planet?
d) What is the frequency detected by each ship and by the planet (3 answers)?

This is all along a line, so you need Lorentz velocity transformations and Doppler formula along a line: u =( u′+v) /(1+((u ′ v)/ c^2)) and f′ = fq1±β 1∓β Keeping signs straight is non-trivial here.

Answer 1