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Question

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?

Answer 1

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.