trajectory of a bullet

[Jon G.]

Three spheres of known centers and known radii intersect at 2 points. This
Excel 97 Worksheet calculates the 2 points:

http://www.geocities.com/jongiff2000/GPS_math.xls

Simply enter the coordinates of the 3 centers and 3 radii, and the Excel
program calculates the coordinates of the 2 points instantly.

Save the Excel file if you'd like and use it for your applications.

For instance, suppose you have a tripod with two fixed legs and one
adjustable leg. The location of the vertex of the tripod can be calculated
from the lengths of the 3 legs and the coordinates of their bases.

===

A gunshot sends a bullet at Mach n sweeping out a cone of half angle c.
Three microphones of known coordinates pick up the shock wave at known time
differences. From this information, what are the coordinates of the gunman?
Find the trajectory of the bullet and predict where it will go before it
gets there.

This problem has been solved and its solution is known and used on
helicopters by the military. Can you solve it? I've tried and I can't.
Find the vector equation, differentiate it with respect to time, and go from
there.

A 4th microphone is used to determine if the gunshot originated from above
or below the plane of the first 3.