Solve the problem.
-Two recording devices are set 2,800 feet apart, with the device at point A to the west of the device at point B. At a point on a line between the devices, 400 feet from point B, a small amount of explosive is detonated. The
Recording devices record the time the sound reaches each one. How far directly north of site B should a second
Explosion be done so that the measured time difference recorded by the devices is the same as that for the first
Detonation?
A) 430.77 feet
B) 5562.37 feet
C) 1142.61 feet
D) 1486.61 feet

Question

Quizplus · Accepted Answer

For the sound to have the same time difference at both devices, the second explosion must be on the same hyperbola as the first. The distance from the first explosion to B is 400 feet, making it 2400 feet from A (since A and B are 2800 feet apart). The hyperbola's equation relating the distances to A and B (x and y) is |x - y| = 2400 - 400 = 2000. For a point directly north of B, the distances to A and B form a right triangle with the segment connecting A and B. Using the Pythagorean theorem, if d is the northward distance from B, then (2400 + d)^2 - (400 + d)^2 = 2000^2. Solving for d gives approximately 430.77 feet.

Solve the Problem. -Two Recording Devices Are Set 2,800 Feet Apart, with the Apart