A Supersonic Fighter Jet Speed Calculation

Calculating the Speed of a Supersonic Fighter Jet

A supersonic fighter jet flies directly over the top of a person on the ground. When the person hears the jet, they look up and see that the jet is 44.8 degrees above the flat horizon. If the speed of sound in air is 340 m/s, what is the speed of the jet?

Final answer:

The speed of the jet is approximately 438.6 m/s.

Explanation:

To calculate the speed of the jet, we can use the concept of the Doppler effect. The Doppler effect is the change in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave. In this case, the sound waves emitted by the jet are affected by the motion of the jet and the observer on the ground.

When the person on the ground hears the jet, they look up and see that the jet is 44.8 degrees above the flat horizon. This angle is known as the angle of elevation. We can use trigonometry to relate this angle to the speed of the jet.

Let's assume that the speed of the jet is v. The speed of sound in air is given as 340 m/s. We can use the tangent function to relate the angle of elevation to the speed of the jet:

tan(angle) = (speed of jet) / (speed of sound)

Substituting the given values:

tan(44.8) = v / 340

Solving for v:

v = 340 * tan(44.8)

Using a calculator, we find that the speed of the jet is approximately 438.6 m/s.