Cartesian Vectors: Calculate Magnitude & Direction

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SUMMARY

The discussion focuses on calculating the resultant force of two football kicks using vector analysis. Andrew applies a force of 155N, while David applies 210N at a 30-degree angle to each other. The magnitude of the resultant force is calculated as 108.38N using the cosine law. The confusion arises regarding the direction of the resultant force, specifically why the book references cos 150 degrees, prompting further exploration of vector orientation and the sine law.

PREREQUISITES
  • Understanding of vector addition and forces
  • Familiarity with the cosine law for triangle calculations
  • Knowledge of the sine law for angle determination
  • Basic trigonometry concepts
NEXT STEPS
  • Study the application of the cosine law in vector addition
  • Learn how to apply the sine law to find unknown angles in triangles
  • Explore vector diagrams and their quadrants for better visualization
  • Investigate the implications of vector direction on resultant forces
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and vector analysis, as well as educators seeking to clarify vector addition concepts.

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Homework Statement



Andrew and David kick a football at the same time. Andrew kicks it with a force 155N and David kicks it with a force 210N. Angle between the two forces is 30 degrees. Calculate the magnitude and direction of the resultant force.

Homework Equations



Cosine law



The Attempt at a Solution



Magnitude = Sqrt (1552 + 2102 - 2(155)(210)cos30 )
= 108.38N

Direction: Use sine law

I don't understand why the answer at the back of the book used cos 150.

If I were to draw the diagram, would the 2 vectors appear in quadrant 2?

Are they assuming that one of the vectors is parallel to the x axis? (like this):

cartesian.jpg


I was assuming that the vectors were at an angle to the x axis...
 
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It doesn't matter what direction they punt in. Look at this picture:

vectors.jpg


You have figured out r. In the triangle with angle a you know all three sides. If you want to use the law of sines, what angle do you know besides the unknown a? That might answer your question.
 

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