Forces in Two Dimensions - Mission F2D1 Detailed Help

A vector is shown in the diagram below. This vector has two components. The ____ component would be greater than the ____ component.


 
Definition of Vector Component
A vector component is a projection of a vector onto the horizontal or vertical axis.


 
The components of a vector are often represented on a diagram by constructing a right triangle about the vector such that the vector is the hypotenuse of the right triangle. The components are then the legs of the right triangle. (You have likely seen such diagrams and might make an effort to sketch one now.) If the vector is a northeast vector, then it has components stretching east and north. The east and north components are simply the east and north legs of the triangle which has been created from the northeast vector. If you wish to compare the magnitudes of the two components, simply compare the length of the legs on the triangle. The leg which is biggest (either the east-west leg or the north-south leg) is the component which is biggest.


 
The first step to successfully answering this question involves determining the direction of the two vector components - east or west and north or south. Simply look at the given vector and ask In which two directions is this vector pointing?
 
Once you have determined the direction of the two components, begin the comparison of their magnitudes. If a vector is directed northeast at 45 degrees into the first quadrant, then it is directed just as much east as it is north. But if the vector is rotated more than 45 degrees counterclockwise from East (that is more toward the north), then the northern component is bigger than the eastern component. And if the vector is rotated less than 45 degrees counterclockwise from East (that is more toward the east), then the eastern component is bigger than the northern component.
 
What is written here about a northeast component in the first quadrant can be written of any vector in any of the quadrants. The more a vector is rotated towards a given axis, the greater the component along the axis will be.


 

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