Final answer:
To find the time difference between two lightning flashes seen by the assistant, one computes the path length difference and divides by the speed of light. It results in a time difference of 20 microseconds between the two flashes as they each travel different distances to reach the assistant.
Step-by-step explanation:
The scenario provided is a classic physics problem that deals with the constancy of the speed of light and how different observers can perceive events differently based on their relative motion.
To calculate the time difference between the two flashes of lightning as viewed by the assistant, we need to consider the distance each flash has to travel to reach the assistant and the speed of light. Since we're ignoring relativistic effects at these scales, we can simply use the equation Δt = Δd / c, where Δt is the time difference, Δd is the difference in distance each light flash travels to reach the assistant, and c is the speed of light.
If the assistant is standing at x = 3.0 km and lightning bolt 1 is at x = 0 km, then the first flash travels 3.0 km to reach the assistant. The second flash from lightning bolt 2 at x = 12.0 km will travel 9.0 km to reach the assistant. The difference in distance (Δd) between the two paths of light is 6.0 km or 6,000 meters. More formally:
Δd = distance from lightning bolt 2 to assistant - distance from lightning bolt 1 to assistant
Δd = 9.0 km - 3.0 km
Δd = 6.0 km
Δd = 6,000 m
Using the speed of light c = 3 × 108 m/s, we calculate the time difference (Δt) as follows:
Δt = Δd / c
Δt = 6,000 m / (3 × 108 m/s)
Δt = 2 × 10-5 s or 20 µs
Therefore, the time difference between the two flashes as seen by the assistant is 20 microseconds.