Question: 51. In the LORAN (LOng RAnge Navigation) radio navigation system, two radio stations located at and transmit simultaneous signals to a ship or an aircraft

51. In the LORAN (LOng RAnge Navigation) radio navigation system, two radio stations located at and transmit simultaneous signals to a ship or an aircraft located at . The onboard computer converts the time difference in receiving these signals into a distance difference , and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure). Suppose that station B is located 400 mi due east of station A on a coastline. A ship received the signal from B 1200 microseconds before it received the signal from A.

(a) Assuming that radio signals travel at a speed of 980 ft $s, find an equation of the hyperbola on which the ship lies.

(b) If the ship is due north of , how far off the coastline is the ship?

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