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Home Minds On Vectors and Projectiles Mission VP5 Vector Components Help Help 9

Mission VP5 Vector Components

The Question

A 50-N force is applied at 30 degrees (sometimes called 30 degrees north of east). This would be the same as applying two forces at ... .

Minds On Time

Mathematically, a vector component is the projection of a vector onto the x- and y-axes. In terms of Physics, a vector component describes the effect of a vector in a given direction. A northeast force vector has the effect of pushing or pulling an object both northward and eastward. Together, the two components of the vector are an equal substitute for the vector itself. The actual vector could be replaced by its two components and the result would be the same. To answer this question correctly, simply determine the components of the given vector (see Think About It section).

Think About It

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 you 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 that has been created from the northeast vector.
 
Trigonometric functions can be used to determine the precise magnitude of the legs of these triangles. If the angle Thetais the angle between the eastern axis and the vector, then the leg adjacent the angle Thetais the x-component and the leg opposite the angle Thetais the y-component. Thus, the cosine function is used to calculate the x-component and the sine function is used to calculate the y-component. See Math Magic section.

Math Magic

SOH CAH TOA
The trigonometric functions sine, cosine and tangent can be used to express the relationship between the angle of a right triangle and the lengths of the adjacent side, opposite side and hypotenuse. The meaning of the three functions are:
 
sine Theta= (length of opposite side / length of hypotenuse)
cosine Theta= (length of adjacent side / length of hypotenuse)
tangent Theta= (length of opposite side / length of adjacent side)

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