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Part 1
Suppose that two people standing 3 miles apart both see the burst from a fireworks display. After a period of time, the first person, standing at point A, hears the burst. One second later, the second person, standing at point B, hears the burst. If the person at point B is due west of the person at point A, and if the display is known to occur due north of the person at point A, where did the fireworks display occur? Note that sound travels at 1100 feet per second. How many feet north is the fireworks display from the person at Point A?
To solve this problem, we need to first calculate the time it takes for the sound wave to travel from the fireworks display to point A and point B.
The time it takes for the sound wave to reach point A after the burst is heard by the person at point B is 1 second. This means that the sound wave had to travel the distance between point A and B in that 1 second. Since the distance between point A and B is 3 miles (5280 feet per mile), the time it takes for the sound wave to travel from point A to point B is 3 * 5280 feet / 1100 feet per second = 14.4 seconds.
Now that we know it takes 14.4 seconds for the sound wave to travel from A to B, we can use this information to determine the distance from point A to the fireworks display. In 14.4 seconds, the sound wave travels the same distance from point A to the fireworks display as it does from point A to point B. Therefore, the fireworks display is 14.4 * 1100 feet = 15840 feet directly north of point A.