Final answer:
To determine the time at which firecracker 1 exploded, we need the speed of light to calculate how long it took the light to travel from the firecracker to Bjorn. The time difference between the light from firecracker 1 and firecracker 2 reaching Bjorn would give us the time difference between their explosions. However, without the time of explosion for firecracker 2, we cannot calculate the exact time of explosion for firecracker 1.
Step-by-step explanation:
The student's question pertains to the calculation of the time at which firecracker 1 explodes, given that Bjorn is standing at x = 500 m and the explosion flashes from both firecrackers reach Bjorn's eyes at t = 4.0 μs. To solve this problem, we need to use the physics concept that light travels at a constant speed (approximately 3 × 10^8 m/s in a vacuum). Since we know the distances of Bjorn to both firecrackers, we can calculate the time it took for the light from each firecracker to reach him.
Given that firecracker 2 is at x = 950 m, the light from firecracker 2 travels 950 m - 500 m = 450 m to reach Bjorn. Similarly, the light from firecracker 1 travels 500 m to reach Bjorn since it exploded at the origin. Knowing the speed of light, we can find the time taken for the light to cover these distances:
Time for light from firecracker 1: t1 = 500 m / (3 × 10^8 m/s)
Time for light from firecracker 2: t2 = 450 m / (3 × 10^8 m/s)
The difference in these times is equal to the time difference between the explosions of the two firecrackers. Since both flashes reach Bjorn at the same time, we can set up the following equation:
Time of explosion of firecracker 1 + t1 = Time of explosion of firecracker 2 + t2