Shock Waves Traveling to the Ground from a Jet

AI Thread Summary
A jet flying at 3300 m altitude creates a shock wave with a 43-degree angle, leading to questions about the time it takes for the sonic boom to reach the ground and the distance the jet travels during that time. The initial calculation attempted to determine the distance sound travels by using the sine function, but the result of approximately 14 seconds was deemed incorrect. The discussion highlights the importance of understanding the geometry of shock waves and their relationship to the jet's speed. The angle of the shock wave is directly influenced by the jet's speed, affecting both the timing and distance calculations. Clarifying these concepts is crucial for accurately solving the problem.
Barry Melby
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A jet flying directly over you at an altitude of 3300 m produces a shock wave. The angle of the shock wave is 43 degrees. How long will it be until the sonic boom reaches you? How far does the jet travel during this time interval?

I know that I can figure out the second part of this problem if I get the first part, but I am not getting the correct answer for the first part.

For the first part I took 3300/sin(43) to get the total distance for the sound to travel to the ground. I then took this number and divided it by 343 m/s (speed of sound) to get approximately 14 seconds, but this appears to be wrong. Where did I go wrong?
 
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The shock wave is a cone traveling with and trailing behind the airplane.
 
Please don't delete the HW template when posting a HW thread.

What's the relationship between the speed of the plane and the angle of the shock wave?
 
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