Final answer:
Regardless of the spaceship's speed, an Earth-bound observer measures the speed of the light pulse as 'c', the constant speed of light, due to relativity. Option number C is correct.
Step-by-step explanation:
An observer on Earth would measure the speed of a light pulse within a spaceship moving at a constant speed of 0.5c (half the speed of light). According to the principles of Einstein's theory of relativity, the speed of light is constant and does not change relative to the motion of the light source.
Therefore, regardless of the speed at which the spaceship is traveling, the speed of the light pulse as observed from the Earth will always be c, the speed of light in a vacuum, which is approximately 299,792 kilometers per second (about 186,282 miles per second).