To use geometric and component addition of vectors. Four vectors A , B , C , and

Question

To use geometric and component addition of vectors.

Four vectors A, B, C, and D are shown (not to scale). Vector A has magnitude 22.1 and acts at an angle of 14.5 degrees with respect to the positive x axis. Vector Bhas magnitude 11.7 and acts at an angle of 67.9 degrees with respect to the positive x axis. Vector C has magnitude 46.3 and acts at an angle of 146.7 degrees with respect to the positive x axis. Vector D has magnitude 15.0 and acts at an angle of 288.1 degrees with respect to the positive x axis.

What is the resultant vector, R, obtained by adding vectors C and D?

Now we wish to add all four vectors. Attempting to do this using the parallelogram method is difficult because that method is optimized for two vectors. It is much easier to use vector components when there are more than two vectors being added.

For the vector sum R=A+B+C+D, what are the magnitude and direction of the resultant R?

Explanation / Answer

net force in y direction = 22.1 * sin(14.5) + 11.7 * sin(67.9) + 46.3 * sin(146.7) + 15.0 * sin(288.1)

= 27.54 N

net force in x direction = 22.1 * cos(14.5) + 11.7 * cos(67.9) + 46.3 * cos(146.7) + 15.0 * cos(288.1)

= -8.24 N

Net force = -8.24 i + 27.54 j

or

826.35 N at an angle of 176.66 degrees from positive x axis

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