Hyperbola Word Problems?
Two recording devices are set 2400 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, 300 feet from point B, a small amount of explosive is detonated. The recording devices record the time until the sound reaches each. 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? Please, show solution steps.
- PuzzlingLv 73 months agoFavorite Answer
The ratio of the distances from the original explosion is 7:1.
If you put a new set of explosive 'x' feet north of B, it with be 7x feet away from A along the hypotenuse of a right triangle. The base will be 2400 feet.
Using the Pythagorean theorem:
x² + 2400² = (7x)²
48x² = 2400²
x = 2400/√48
x ≈ 346.4 ft