An observer at sea level does not hear an aircraft that is flying at an altitude of 7000 m until it is a distance of 13 km from the observer. Estimate the Mach number at which the aircraft is flying. Assume that the average temperature of the air between sea level and 7000 m is –10°C.

[tex]C = \sqrt{kRT} = \sqrt{(1.4) (287) (163)} = 325.1 m/s\\\\tan \alpha = \frac{7000}{13000} = 0.5385\\\alpha = 28.3\\\\M = \frac{1}{sen \alpha } = 2.109[/tex]

Answer Link

riwa5534 riwa5534 · Answer 2 · 2025-04-09T19:34:44-04:00

Final answer:

The Mach number at which the aircraft is flying is approximately 39.27.

Explanation:

The Mach number of an aircraft can be estimated using the formula:

Mach number = velocity of the aircraft/speed of sound

First, we convert the altitude to meters: 7000 m

The speed of sound at -10°C is approximately 331 m/s

The distance at which the observer at sea level hears the aircraft is 13 km which is equal to 13,000 m

Using the formula:

Mach number = distance / time

Substituting the values:

Mach number = 13,000 m / time

Since the observer doesn't hear the aircraft until it is a distance of 13 km, we can assume the time it takes for the sound to reach the observer is the same as the time it takes the aircraft to cover the distance of 13 km.

Therefore, the Mach number at which the aircraft is flying is approximately 39.27.