Final answer:
The constant speed of light for all observers results in time dilation, where the spacecraft pilot experiences slower time relative to the Earth-bound .
observer, making option (c) 'time for the pilot would pass slower than for the observer' the correct choice.
Step-by-step explanation:
In this scenario, regardless of the relative motion of the spacecraft and the observer, the speed of light remains constant for all observers in all inertial frames of reference, as per the principles of special relativity. Therefore, neither option (a) 'the speed of light for the observer would be greater' nor (b) 'the speed of light for the observer would be smaller' is correct. Instead, due to the effects of time dilation.
This is because from the Earth observer's point of view, the clocks on the spacecraft are moving slower due to its high speed relative to the Earth. Conversely, for the pilot of the spacecraft, their experience of time would be normal, but they would observe Earth's clocks to be moving faster. However, it is critical to understand that these observations are relative; each observer sees the other's clock as ticking at a different rate due to the relative motion between them.
Option (c) 'time for the pilot would pass slower than for the observer' is the correct option.