Two LORAN radio stations A and B are 140 kilometers apart and send a simultaneous radio signal to a ship.

Question

The signal from B arrives 0.0002 seconds before the signal from A. If the signal travels 300,000 kilometers per second, find the equation of the hyperbola on which the ship is positioned. Use a coordinate system where the origin is the midpoint between the stations, and the stations lie on the x-axis.

Answer 1

2c = 140 km; c = 70 km; 2a = 300000·0.0002 km = 60 km; c = 30 km; b² = 4900 - 900 = 4000 km².

Equation of hyperbola: x²/4900 - y²/4000 = 1