How far directly north of point 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?
How far directly north of point 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?
How far directly north of point 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?
Expert Solution & Answer
Answer to Problem 78AYU
Solution:
700 feet.
Explanation of Solution
Given:
Two recording devices are set 2400 feet apart, with the device at point to the west of the device at point . At a point between the devices 300 feet from point , a small amount of explosive is detonated. The recording devices record the time until the sound reaches each.
Formula used:
Equation of the hyperbola , .
Calculation:
Set of all points where explosion takes place and the time difference is same, forms a hyperbola with and as the foci.
Since and are foci we have, , .
is on the transverse axis and is on the hyperbola. Hence is the vertex of the hyperbola.
Since it is 300 feet from , .
The equation of the hyperbola is,
The point lies on the hyperbola.
The second explosion should be set up at a distance of 700 feet due north of point .
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