![]() Θ = tan –1 ( A y / A x ) θ = tan –1 ( A y / A x ). Those paths are the x- and y-components of the resultant, R x R x and R y R y. In particular, the person could have walked first in the x-direction and then in the y-direction. There are many ways to arrive at the same point. The person taking the walk ends up at the tip of R. If A A and B B represent two legs of a walk (two displacements), then R R is the total displacement. ![]() You can use analytical methods to determine the magnitude and direction of R R. For example, given a vector like A A in Figure 3.24, we may wish to find which two perpendicular vectors, A x A x and A y A y, add to produce it.įigure 3.28 Vectors A A and B B are two legs of a walk, and R R is the resultant or total displacement. We very often need to separate a vector into perpendicular components. Resolving a Vector into Perpendicular ComponentsĪnalytical techniques and right triangles go hand-in-hand in physics because (among other things) motions along perpendicular directions are independent. Analytical methods are limited only by the accuracy and precision with which physical quantities are known. However, analytical methods are more concise, accurate, and precise than graphical methods, which are limited by the accuracy with which a drawing can be made. Part of the graphical technique is retained, because vectors are still represented by arrows for easy visualization. Apply analytical methods to determine the magnitude and direction of a resultant vector.Īnalytical methods of vector addition and subtraction employ geometry and simple trigonometry rather than the ruler and protractor of graphical methods.Apply analytical methods to determine vertical and horizontal component vectors.Understand the rules of vector addition and subtraction using analytical methods.By the end of this section, you will be able to:
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