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.

1 Answer

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  • 3 months ago
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    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

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