Lab 3: Vector Addition Purpose To use simulation of vector addition to nd the resultant of two vectors and compare the results to that obtained by analytical method. Background A quantity such as velocity, which has direction as well as magnitude, is a vector quantity. _) Consider a vector A that lies in the aggzplane. Its magnitude is A and points at an angle 8 from .} the x axis. Vector A can be resolved into two other vectors along the x and y axes, called components. The x and y component are given by: A, = A0036 Ay = Asing The vector that results from the addition of two vectors or more is known as the resultant a vector R such that, > -9 > R = A + B 6 The components of R are given by: RJr = A, + Bx R}, = A}. + By ) The magnitude R and direction Q5 of R can be calculated by applying trigonometry and the Pythagorean Theorem: __ 2 ' 2 RM&+& R ()5 = tan\" __v I Rx Procedure A. Simulation 1. Click on this simulation link (ht; --> . B as shown: in the diagram: Vector Length Direction > A 50 20' __) B 100 ~75' 2. Use the sliders or input boxes to change the length and direction of the blue and orange vectors. When the "addition" checkbox is selected, the black vector shows the vector sum of the blue and orange vectors [A + B}. Enter the magnitude R and direction ()5 of ii in Table 1. Table 1. Simulation iVector 'Length Direction ' __, , R B. Components Method 1. For each vector shown in the diagram, calculate the x- and y components and record these values in Table 2. > > Table 2. Components of A and B Vector x-component ycomponent .9 A _) B _) 2. Add the two vectors to calculate the components ofthe resultant vector R. Record your ndings in Table 3. .9 Table 3. Components of R R V l' R a I _\\ 3. Calculate length and direction of the resultant vector. Record your ndings in Tibia 4. Table 4. Resultant Vector Length Direction > R 4. Calculate the percentage difference in R. R R i a, %difference = measured calculate ' X 100 Realculared Reporting _ After completing your data analysis, type your ndings in the provided Lab Report 3 and submit for grading