The ship’s bearing and distance from point
It has been determined that the cruise ship Princess Ann is about
Given:
Three LORAN radio transmitters are positioned as shown in the figure, with
Concept used:
The speed of radio signals is
The difference between distances from the foci to any point on the hyperbola, is constant.
Calculation:
It can be seen from the figure that
Now, the speed of radio signals is
Then, the speed of radio signals is
Denote the position of the cruise ship as
It is given that the time difference between the reception of signals from
Then, it follows that,
Now, the set of all possible points such that
It is given that
This is nothing but the distance between two foci of the hyperbola.
So,
Now,
So,
Now, the center of the hyperbola is at the midpoint of
Then, the equation of the hyperbola is,
Put
Similarly, it is given that the time difference between the reception of signals from
Then, it follows that,
Now, the set of all possible points such that
It is given that
This is nothing but the distance between two foci of the hyperbola.
So,
Now,
So,
Now, the center of the hyperbola is at the midpoint of
Then, the equation of the hyperbola is,
Put
So,
Graphing the hyperbolas, the first quadrant point of intersection of these hyperbolas, such that the point of intersection is out in the sea, is
Now, the bearing of
The distance of
Conclusion:
It has been determined that the cruise ship Princess Ann is about
Chapter 8 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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