I I Know Where You Are !

Student Worksheet - GPS Challenge

Your challenge is to locate specific points on a map with the same methods used by the Global Positioning System. You will need a printed copy of “TriumphMap.pdf.” (see Appendix A, How To Get A Topographic Map for information on downloading this file.) This is a portion of a U.S. Geological Survey topographic map covering the vicinity of Triumph, Idaho, an historic mining town.

  1. Three GPS satellites are used for this challenge. The position of GPS Satellite #1 corresponds to the upper right corner of the map (about 43°39’46”N, -114°13’30”W). The position of GPS Satellite #2 corresponds to the lower right corner of the map (about 43°37’59”N, -114°13’30”W). The position of GPS Satellite #3 corresponds to the lower left corner of the map (about 43°37’59”N, -114°16’30”W). Draw a small circle at each of these locations, and label the circle with the appropriate GPS Satellite number.

  2. Table 1 shows the distances to GPS Satellites #1, #2 and #3 from various points on the map. To locate a given point, use a drawing compass to construct an arc that is centered on GPS Satellite #1 with a radius equal to the distance shown in Table 1. If your compass won’t open enough to set the given distance, you can use a piece of string tied between two pencils to draw the arc. Next, construct a second arc centered on GPS Satellite #2 with the radius shown in Table 1. Finally, construct a third arc centered on GPS Satellite #3 with the radius shown in Table 1. The intersection of the three arcs is the location of the given point. If the arcs do not coincide exactly (they usually don’t), use the center of the overlap area as the approximate location of the point.

  3. Repeat this process to answer the following questions:

a. What features are shown near the following points:

     (1) Point 1: _________________________

     (2) Point 2: _________________________

     (3) Point 3: _________________________

     (4) Point 4: _________________________

     (5) Point 5: _________________________

     (6) Point 6: _________________________

     (7) Point 7: _________________________

b. What is the elevation of Point 8? _______________________

c. You are looking for a benchmark whose location is supposed to be Point 9. Why may this benchmark be difficult to recover? _________________________________________

d. What is the elevation of Point 10? ______________________

Table 1

Location          Distance from          Distance from          Distance from
              GPS Satellite #1    GPS Satellite #2    GPS Satellite #3
                  (inches)             (inches)             (inches)

Point 1               10.1                    9.5                    4.4

Point 2               3.4                    4.4                   12.0

Point 3               11.5                   12.4                    5.5

Point 4               8.5                    9.8                    6.5

Point 5               8.7                    8.1                    4.4

Point 6               6.4                    5.8                    8.3

Point 7               9.1                    8.2                    5.4

Point 8               12.0                   11.5                    3.1

Point 9               10.2                    8.9                    4.2

Point 10               11.2                   12.9                    6.7


 

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