Question

Two geological field teams are working in a remote area. A global positioning system (GPS) tracker at their base camp shows the location of the first team as 37 km away, 21° north of west, and the second team as 33 km away, 32° east of north. When the first team uses its GPS to check the position of the second team, what does it give for the second team's (a) distance from them and (b) direction, measured from due east?

Answer 1

We are given vectors A and B. We need to find vector C, which from the above diagram could be written as C = B - A. So we can find this if we find x and y components and then find C's x and y-components.

A_x = A cos (_A)

A_y = A sin (_A)

B_x = B cos (_B)

B_y = B sin(_B)

From the way the angles are provided in the problem, A is given as 19° North of West, this will be written as 180° -19° as 180° is due West and subtracting moves you North of West. B is given as 35° East of North, so it will be written as 90°- 35°. so our components are:

A_x = A cos (_A) = (38km)cos(180°-19°) = -35.9km

Note, since this points west, on our coordinate system it should be negative.

A_y = A sin (_A) = (38 km)sin(180°-19°) = +12.4km

B_x = B cos (_B) = (29km)cos(90° - 35°) = +16.6km

B_y = B sin(_B) = (29km)sin(90° - 35°) = +23.8 km

As mentioned earlier, we know C = B - A, so we find the x and y components of C as follows:

C_x = B_x - A_x = 16.6 km - (-35.9 km) = 52.5 km

C_y = B_y - A_y = 23.8km - (12.4km) = 11.4 km

Now we can use the Pythagorean theorem to find magnitude and direction of C

So the displacement vector from Team #1 to Team #2 is

C = 54 km @12°N of E