Two geological field teams are working in a remote area. A Global Positioning Sy

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 degrees north of west. The second team is 24 km away, 34 degrees east of north. When the first team uses its GPS to check the position of the second team, what does the GPS give for the following?
A) the second team's distance from the first team (in km)
B) the second team's direction from the first team, measured relative due east 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 degrees north of west. The second team is 24 km away, 34 degrees east of north. When the first team uses its GPS to check the position of the second team, what does the GPS give for the following?
A) the second team's distance from the first team (in km)
B) the second team's direction from the first team, measured relative due east
A) the second team's distance from the first team (in km)
B) the second team's direction from the first team, measured relative due east

Explanation / Answer

here ,

let east be x direction

north be positive y direction

A)

position of first team

r1 = 37 * (- cos(21) i + j * sin(21)) km

r1 = -34.5 i + 13.3 j km

position of second team

r2 = 24 * (sin(34) i + j * cos(34))

r2 = 13.24 i + 19.9 j km

Now , for the position of second team relative to first team

r21 = r2 - r1

r21 = 13.24 i + 19.9 j - (-34.5 i + 13.3 j)

r21 = 47.74 i + 6.6 j km

r21 = sqrt(47.74^2 + 6.6^2) at arctan(6.6/47.74) degree north of east

r21 = 48.2 km at 7.87 degree north of east

distance between two teams is 48.2 km

b)

the direction of first team is 7.87 degree north of east

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