If a spaceship is travelling at half the speed of light and is ten kilometres ahead of the light, does the light overtake the spaceship?

Question

I have searched AI chatbots. Some say yes, the light overtakes the spacecraft, others say no.

Answer 1

According to the theory of relativity, the speed of light in a vacuum is constant and is the same for all observers, regardless of their relative motion. This means that the speed of light is always measured to be c = 299,792,458 meters per second, regardless of the motion of the observer or the source of the light.

In this scenario, the spaceship is traveling at half the speed of light, which means its velocity is v = 0.5c. If the spaceship is 10 kilometers ahead of the light, we can calculate the time it would take for the light to reach the spaceship using the equation:

time = distance / speed

The distance between the spaceship and the light is 10 kilometers, or 10,000 meters. The speed of light is c = 299,792,458 meters per second. So the time it would take for the light to reach the spaceship is:

time = 10,000 / 299,792,458 = 0.000033 seconds

Now, let's consider how far the spaceship travels during this time. Since the spaceship is traveling at half the speed of light, its velocity is v = 0.5c. So in 0.000033 seconds, the spaceship would travel:

distance = speed x time = 0.5c x 0.000033 = 4,993 meters

This means that during the time it takes for the light to travel 10 kilometers, the spaceship would have traveled almost 5 kilometers. Therefore, the light would not overtake the spaceship in this scenario.