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

In summary, the first team is located 38 km away, 19° north of west, while the second team is 29 km away, 35° east of north. To find the distance and direction between the teams, we need to calculate the vector difference between the two teams. Using the equations Fx = Fax + Fbx and Fy = Fay + Fby, we can determine that the resultant vector is 40.95723706 meters and the direction, Θ, is 61.89263517 degrees north of west. However, this is not the correct answer as we need to find the distance and direction from due east. To do this, we need to calculate the vector difference between the teams, which
  • #1
jehan4141
91
0
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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  • #2
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.
 
  • #3
Isn't A+B the distance between A and B?
 
  • #4
I drew a diagram from the very beginning and still don't see my error.
 
  • #5
Isn't A+B the distance between A and B?
No. It is a vector sum. I think you want a vector difference.
 

1. What is vector component addition?

Vector component addition is a mathematical operation used to combine two or more vectors into a single vector. It involves breaking down each vector into its horizontal and vertical components, and then adding them together to find the resultant vector.

2. Why is vector component addition important?

Vector component addition is important because it allows us to analyze and understand the motion of objects in different directions. It is also used in many fields of science, such as physics, engineering, and navigation.

3. How is vector component addition different from vector addition?

Vector component addition is different from vector addition because it involves breaking down vectors into their components and then adding them together, whereas vector addition simply involves adding the magnitudes and directions of two or more vectors together.

4. What are some real-life applications of vector component addition?

Some real-life applications of vector component addition include calculating the displacement and velocity of objects moving in two dimensions, determining the net force acting on an object, and solving problems in navigation and engineering.

5. Can vector component addition be applied to vectors in three dimensions?

Yes, vector component addition can be applied to vectors in three dimensions by breaking them down into their x, y, and z components and then adding them together. This allows for the analysis of motion and forces in three-dimensional space.

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