How Do You Calculate Vector Components and Resultant Displacement?

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To calculate vector components and resultant displacement, one must first determine the x and y components of a given vector using trigonometric functions. For the first vector with a magnitude of 810m at 18 degrees, the x component is found using cosine, and the y component using sine. The second vector, 23 km at 65 degrees south of east, similarly requires the application of these functions to find its components. The resultant displacement for the four members of the bicycle club can be calculated by summing their individual displacement vectors. Understanding vector components is essential for solving these types of problems effectively.
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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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