Question

spaceships a and b are traveling directly toward each other at a speed 0.5 c relative to the earth, and each has a headlight aimed toward the other ship. part a what value do technicians on ship b get by measuring the speed of the light emitted by ship a's headlight?

Answer 1

v1 = speed of light emitted by ship a (travelling + towards b)

V = speed of earth frame as measured by ship b

v2 = speed of light measured by observer in ship b

v2 = (v1 - V) / (1 - V v1 / c^2) velocity transformation

v1 = c

V = -c / 2 speed of earth measured in b

v2 = speed observed by observer in b

v2 = (c + c/2) / (1 - c * (-c/2)c^2)

v2 = 3 c/2 / (3 / 2) = c

v2 measures speed c emitted by light in frame a