Calculating Distance and Direction Between Two Teams in a Remote Area Using GPS

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Homework Help Overview

The problem involves calculating the distance and direction between two geological field teams using GPS coordinates. The first team's position is given as 38 km away at 19° north of west, while the second team is 29 km away at 35° east of north. The original poster seeks to determine the distance and direction from the first team to the second team based on these coordinates.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to use vector addition to find the distance and direction between the two teams. Some participants suggest reconsidering the approach, indicating that a vector difference may be more appropriate. Others question the interpretation of vector addition in this context.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of vector addition versus vector difference. Some guidance has been offered regarding the need for a diagram to clarify the situation, but no consensus has been reached on the correct approach.

Contextual Notes

There is a mention of provided answers that differ from the original poster's calculations, indicating potential misunderstandings in the setup or calculations. The original poster expresses confusion about where their reasoning may have gone wrong.

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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 38 km away, 19° north of west, and the second team as 29 km away, 35° 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 distance between the teams and direction,θ, measured from due east?



Homework Equations


Fx = Fax + Fbx
Fy = Fay + Fby

Resultant vector = sqrt[ (Fx2 + Fy2 ]

Θ = tan-1 (Fy/Fx)


The Attempt at a Solution


Fx = -38cos19 + 29cos55 = -19.29598922
Fy = 38sin19 + 29sin55 = 36.12699915

Resultant vector = sqrt [ (-19.29598922)2 + (36.12699915)2]
Resultant vector = 40.95723706 meters

Θ = tan-1(36.12699915/-19.29598922)
Θ = 61.89263517 degrees N of W

Those are my answers but apparently they are wrong. The provided answers are 53.8 km, 12.2 ° from east. Where am I going wrong? Thank you in advance :)
 
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You determined A + B. I think you want B with respect to A. Draw a diagram of what is going on and you may see the solution.
 
Isn't A+B the distance between A and B?
 
I drew a diagram from the very beginning and still don't see my error.
 
Isn't A+B the distance between A and B?
No. It is a vector sum. I think you want a vector difference.
 

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