# Individual Research Projects Section 15.4

### Project 15.4

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.

### Project 15.6

Write a short paper exploring the concept of the eccentricity of an ellipse. The figure shown here shows some ellipses with the same vertices, but different eccentricities.