Ships at sea locate their positions using the Long Range
Navigation system known as LORAN. In this system,
a master station sends signals that can be received by
ships at sea. To fix the position of a particular ship,
a secondary sending station also emits signals that can
be received by the ship. Since the ship monitoring
the two signals will usually be nearer one of the two
stations, there will be a difference in the distances
that the two signals travel. Because d = rt,
there will be a slight time difference between the signals.
If the ship follows a path so that the time difference
remains constant, what is the path the ship will follow?
Suppose the difference in the arrival of the time signals
is 300 microseconds. (Note: a microsecond
is one millionth of a second.) Also, suppose
that the foci are 100 miles apart. Finally, suppose
that signals travel at 980 ft/sec.
