Resultant displacement of vectors

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SUMMARY

The discussion focuses on calculating the resultant displacement of vectors given specific magnitudes and directions: 12.3m North, 45.6m East, 78.9m West, and 14.7m South. The correct approach involves determining the net displacement in both the x (East-West) and y (North-South) directions, resulting in a total displacement of 33.4m and an angle of 184.1 degrees when adjusted for the correct quadrant. The use of the Pythagorean theorem and trigonometric functions, specifically the tangent inverse, is essential for accurate calculations.

PREREQUISITES
  • Understanding of vector addition and subtraction
  • Familiarity with the Cartesian coordinate system
  • Knowledge of the Pythagorean theorem
  • Basic trigonometry, specifically tangent and inverse tangent functions
NEXT STEPS
  • Study vector addition techniques in physics
  • Learn about Cartesian coordinates and their applications
  • Explore the Pythagorean theorem in two-dimensional space
  • Review trigonometric functions and their use in vector analysis
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Students studying physics or mathematics, particularly those focusing on vector analysis and displacement calculations.

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Homework Statement


Find the resultant displacement(magnitude and direction of the following vectors: 12.3m North, 45.6m East, 78.9m West, 14.7m South


Homework Equations



c=sqrt a^2 + b^2

The Attempt at a Solution


Do you just add the vectors so the north and south added together will give you 2.4m, etc then use Tan inverse to get the angle? when I did that... I got 33.4m for the magnitude and 85.9 degrees for the direction , however do you need to minus that from 270 to get 184.1 degrees? Am i doing this right?
 
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Draw a diagram and show us
 
Crake said:
Draw a diagram and show us

i just drew it on a cartesian plane so it is in the third quadrant.. the y-axis is -2.4m and the x-axis is -33.3m I got those numbers from adding the directions together.
 

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