How Do You Calculate Vector Components and Resultant Displacement?

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SUMMARY

This discussion focuses on calculating vector components and resultant displacement using specific examples. The first problem involves a displacement vector of 810m at an angle of 18 degrees, requiring the calculation of its x and y components. The second problem presents a 23 km vector directed 65 degrees south of east, necessitating similar component calculations. Lastly, the resultant displacement of four members of the Main Street bicycle club is determined by summing their individual vectors: A=2.0km east, B=5.2km north, C=4.9km west, and D=3.0km south.

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  • Familiarity with trigonometric functions (sine and cosine)
  • Knowledge of vector addition techniques
  • Basic geometry concepts related to angles and directions
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Homework Statement


1. A displacement vector has a magnitude of 810m and points at an angle of 18 degrees above the positive x axis, What are the x and y scalar components of this vector?

2. A displacement vector is 23 km in length and directed 65 degrees south of east
What are the components of this vector (East=x South =y)

3. Four members of the Main Street bicycle club meet at a certain intersection on Main Street. The member then start from the same location, but travel in different direction. A short time later, displacement vectors for the four members are:
A=2.0km east B=5.2km north C= 4.9km west D=3.0kmsouth
What is the resultant displacement R for all the members of the bicycle club
r=a+b+c+d



Homework Equations





The Attempt at a Solution


No clue where to start
 
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Well the place to start would be to read up on what is meant by components of a vector. Try looking here, for example.
 

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