Concept explainers
Global Positioning System (GPS) The Global Positioning System determines the location of an object from its distances to satellites in orbit around the earth. In the simplified, two-dimensional situation shown in the following figure, determine the coordinates of P from the fact that P is 26 units from satellite A and 20 units from satellite B.
The coordinates of P from given global positioning system.
Answer to Problem 47E
The coordinates of point P is
Explanation of Solution
Given:
Point P is 26 units far from satellite A and 20 units far from satellite B, and the coordinates of satellite A and B are shows in Figure (1).
The Figure of global positioning system is,
Figure (1)
Calculation:
The formula to find distance between two points
Where, d is distance between two points.
In Figure (1) the coordinates of P is
Substitute 22 for
Further, solve the above equation to get the equation of circle,
In Figure (1) the coordinates of P is
Substitute 28 for
Further, solve the above equation to get the equation of circle,
In the Figure (1), if the radius of planet centered at the corresponding satellite the equation (2) and equation (3) of two circles intersect at a point, thus the equation (2) is equal to the equation (3), solve it for x in y term,
Substitute
Further, solve the above equation to get the value of y,
Two possible value of y give two corresponding values of x.
Substitute 8 for y in equation
Substitute 25.6 for y in equation
Avoid the fractional values of coordinates of point P.
Thus, the coordinates of point P is
Chapter 10 Solutions
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