Explorers' Vector Problem: Can They Communicate After Traveling 5+6 km?

  • Thread starter JSOBOLEW
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In summary, the two teams could not communicate that night because their radios did not have a range of 5 km.
  • #1
JSOBOLEW
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Homework Statement


Two teams of explorers leave a common point. The first team travels 5 km north across a plain, then follows a river 15 degrees west of north for 7 km before making camp for the night. THe second climbs a ridge, traveling basically due northeast for 6 km along a trail that climbs upward to an altitude of 2.5 km. This team then follows the ridge northward at approximately 4 km before making camp for the night. Can the two teams communicate that night if their radios have a range of 5 km?
 
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  • #2
Show your attempted solution.
 
  • #3
Draw a picture showing the paths of both groups. Once you have the picture drawn and distances labled it should be easy.

And yeah, you're suppossed to show relevant equations and your attempted solution.
 
  • #4
Welcome to PF.
Show your attempt.
Are you not getting answer?
Show your calculations in detail.
We will try to printout your mistakes.
 
  • #5
I thought the best course may be to try and find the magnitude of each of the respective teams. So for team one I assigned [5x, 7y, 0z] and for team two [6x, 2.5y, 4z].
If my calculations were right their respective magnitudes should be 8.60233 and 7.63217.

From there I get a bit fuzzy.
Help?

P.S. Sorry for not using the correct symbology with my explanation. I have no idea how to illustrate it on computer.
 
  • #6
You have the coordinates of two points in space just find the distance between the two.
 
  • #7
Jebus_Chris said:
You have the coordinates of two points in space just find the distance between the two.

Right. But that is my question. Nothing is coming to mind that I can use without the help of some other factor (i.e. an angle).
 
  • #8
Unless I consider these points two more vectors and repeat the process...?
 
  • #9
There would be two ways you could do this, essentially the same. You've got a formula, one that you learned a long time ago, but probably haven't used in awhile. It's the distance formula which finds the distance between two points. Or: when you have two values, a and b, and need to find the distance between them you just subtract them.
 
  • #10
So in essence you just take the difference from the respective magnitudes?
 
  • #11
JSOBOLEW said:
So in essence you just take the difference from the respective magnitudes?
These are vectors, you add them via their components.
 

What is the "Tricky Vector Problem"?

The "Tricky Vector Problem" is a mathematical problem that involves finding the magnitude and direction of a vector when given its components in different coordinate systems.

What makes this problem difficult?

This problem is difficult because it requires a deep understanding of vector algebra, coordinate systems, and trigonometry. It also involves multiple steps and calculations, making it easy to make mistakes.

Why is this problem important in science?

Vectors are used in many scientific fields, including physics, engineering, and computer science. The "Tricky Vector Problem" allows scientists to accurately calculate and analyze vector quantities, which are essential in understanding the physical world.

What are some tips for solving this problem?

Some tips for solving the "Tricky Vector Problem" include drawing accurate diagrams, clearly labeling components and angles, using trigonometric identities, and double-checking calculations. It is also helpful to break the problem down into smaller, more manageable steps.

Are there any real-world applications of this problem?

Yes, the "Tricky Vector Problem" has many real-world applications, such as calculating the velocity and direction of a moving object, determining the force and direction of a magnetic field, and analyzing the forces acting on a structure. It is also used in navigation, robotics, and computer graphics.

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