Ground Observer and Sound of Aircraft

How long after the aircraft flies directly above a ground observer is the sound of the aircraft heard by the ground observer?

What factors need to be considered to calculate the time it takes for the sound of the aircraft to reach the ground observer?

Answer:

Approximately 8.75 seconds after the aircraft flies directly above the ground observer, the sound of the aircraft will be heard by the observer.

To determine how long after the aircraft flies directly above a ground observer the sound is heard, we need to consider the speed of sound and the altitude of the aircraft. The speed of sound in air varies with temperature and pressure. In the standard atmosphere, at sea level and at a temperature of 15 degrees Celsius, the speed of sound is approximately 343 meters per second. Since the altitude of the aircraft is given as 3 km (or 3000 meters), we need to account for the additional time it takes for the sound to travel that distance.

The time it takes for the sound to travel from the aircraft to the ground observer can be calculated using the formula:
time = distance / speed

The distance is equal to the altitude of the aircraft, which is 3000 meters. The speed is the speed of sound, which is approximately 343 meters per second. Plugging in the values, we have:
time = 3000 / 343 ≈ 8.75 seconds

Therefore, the sound of the aircraft will be heard by the ground observer approximately 8.75 seconds after the aircraft flies directly above them.