Final answer:
No matter the rocket's velocity, the observed speed of light from the rocket heading toward an observer is always c, the constant speed of light in a vacuum.
Step-by-step explanation:
The question revolves around the concept of the speed of light and how it is perceived by an observer when the light source is moving relative to them. According to Einstein's theory of special relativity, the speed of light in a vacuum is constant and does not change based on the motion of the source or the observer.
Therefore, if a rocket moves directly toward you at a speed of 0.5c and fires a beam of light straight at you, the speed of light that you observe coming from the rocket is still c, the speed of light in a vacuum (approximately 299,792,458 meters per second). This fact remains true regardless of the rocket's velocity with respect to the observer.