Vectors and vector addition Students should review the general discussion of vec

Question

Vectors and vector addition

Students should review the general discussion of vectors given in one of the early chapters of the textbook. You should be able to represent vectors in 2-dimensions graphically and to graphically add two vectors. You should also be able to add vectors analytically and show that it agrees with the graphical solution. Here you are given two vectors, A and B. You will need to write each of these vectors in X-Y components (using unit vectors i and j) and add the vectors to obtain C, the resultant of A and B. You will then express C in polar form, that is its magnitude and direction expressed as an angle wir to the positive x-axis. Then go through the process of graphically adding the A and B vectors (complete the parallelgram method) and show that your graphical solution agrees with your analytical solution.

Explanation / Answer

In order to work with vectors you have to know each vector has two components: the "x" component also known as "i", and the "y" component also known as "j".

A=5i + 1.5j

B=i + 4j

To add two vectors, you only must add the "i" components and the "j" components separately, as you can see:

C=6i + 5.5j

To find the polar components of a vector, you have to apply the following equations:

Polar Form: |C|=(6^2 + 5.5^2)^1/2 = 8.14 <-- This is the norm of a vector

Arg(C) = tan^-1(5.5/6) = 42.5

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