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Mathematics, 26.03.2020 23:20 markel19
An army base in the desert is located at the origin, O of an x-y coordinate system. A soldier at point P needs to determine his coordinates with respect to the army base, but he does not have a link to a global positioning system. He is, however, in radio contact with several small towns in the vicinity. Two of the towns are town A and town B. Town A is 32 miles due south of the army base; town B is 18 miles north of the base. At an agreed-upon instant, both towns send out identifying radio signals. The soldier receives the signal from B slightly before the signal from A, so he knows that he is closer to B than to A. Furthermore, by measuring the time difference between receiving the two signals, the soldier is able to compute that he is 40 miles closer to town B than to town A. Explain why the point P must lie on a certain hyperbola.
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An army base in the desert is located at the origin, O of an x-y coordinate system. A soldier at poi...
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