The velocity of sound in the atmosphere is c=300 m/s. An airplane is traveling with velocity v=600 m/s at an altitude of h=8 km over an observer. How far horizontally past the observer in kilometers will the plane be when the observer first hears the noise of the airplane?
5.4
To find out how far horizontally past the observer the plane will be when the observer first hears the noise of the airplane, we need to determine the time it takes for the sound to reach the observer.
The speed of sound in the atmosphere is given as c = 300 m/s. The airplane is traveling with velocity v = 600 m/s and is at an altitude of h = 8 km.
First, let's calculate the time it takes for the sound to reach the observer:
Time = Distance / Speed
The distance the sound travels is equal to the altitude of the plane, which is h = 8 km = 8000 m.
Time = Distance / Speed = 8000 m / 300 m/s
Simplifying, we have:
Time = 26.67 seconds
Now, since the airplane is moving horizontally at a velocity of 600 m/s, we can calculate the horizontal distance it travels during the time it takes the sound to reach the observer:
Distance = Time * Velocity = 26.67 s * 600 m/s
Simplifying further, we have:
Distance = 16000 m = 16 km
Therefore, the airplane will be 16 km horizontally past the observer when the observer first hears the noise of the airplane.