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Transcribed Image Text:3.
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 with coordinates (-150, 0)
and (150, 0), and that a ship is traveling on a hyperbolic path with coordinates (x, 66) (see
figure 1).
Station
B
-150
-50
100
50
-50
Port
50
Not drawn to scale
Station
A
150
Figure 1
a) Find the x-coordinate of the position of the ship when the time difference between the pulses
from the transmitting stations is 1000 microseconds (0.001 second). (Round your answer to
one decimal place.)
b) Determine the distance between the port and station A. (Round your answer to one decimal
place.)
c) Find a linear equation that approximates the ship's path as it travels far away from the shore.
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