# Long distance radio navigation for aircraft and ships uses synchronized pulses transmitted by widely separated transmitting stations.

Long distance radio navigation for aircraft and ships uses synchronized pulses transmitted by widely separated transmitting stations. These pulses travel at the speed of light (186,000 miles per second). The difference in the times of arrival of these pulses at an aircraft or ship is constant on a hyperbola having the transmitting stations as foci. Assume that two stations, 300 miles apart, are positioned on a rectangular coordinate system at coordinates (-150, 0) and (150, 0), and that a ship is traveling on a hyperbolic path with coordinates (x, 75). (figure on page)A) Find the x-coordinate of the position of the ship if the time difference between the pulses from the transmitting stations is 1000 microseconds.B) Determine the distance between the ship and station 1 when the ship reaches the shoreC) The captain of the ship wants to enter a bay located between the two stations. The bay is 30 miles from the station 1. What should be the time difference between the pulses?D) The ship is 60 miles offshore when the time difference is part c is obtained. What is the position of the ship?