Supersonic Speed Calculation: How Fast Is the Fighter Jet Flying?

What is the speed of a fighter jet flying at an angle of 61.9 degrees above the horizon if the speed of sound in air is 340 m/s? The speed of the jet is calculated by applying the Mach formula which uses the ratio of the speed of the jet to the speed of sound in air. After converting the given angle to radians, the speed of the jet is found to be approximately 660 m/s.

Calculating the Speed of the Fighter Jet:

When a fighter jet flies at a specific angle above the horizon, we can calculate its speed using the Mach formula. In this scenario, the jet is observed at an angle of 61.9 degrees above the flat horizon, and the speed of sound in air is known to be 340 m/s.

First, we need to convert the angle of 61.9 degrees to radians for our calculations. This can be done by multiplying the angle in degrees by π/180. Thus, 61.9 degrees is approximately equal to 1.08 radians.

Next, we will apply the Mach formula, which states that the speed of the jet is equal to the speed of sound divided by the cosine of the angle at which the jet is observed. Mathematically, this can be represented as: speed of jet = speed of sound / cos(theta).

Substituting the values into the formula, we get: speed of jet = 340 m/s / cos(1.08 radians). By solving this equation, we find that the speed of the fighter jet is approximately 660 m/s.

Therefore, the speed of the fighter jet flying at an angle of 61.9 degrees above the horizon is about 660 m/s.
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