o use geometric and component addition of vectors. Four vectors A, B, C, and D a

Question

o use geometric and component addition of vectors. Four vectors A, B, C, and D are shown (not to scale). Vector A has magnitude 21.5 and acts at an angle of 13.1 degrees with respect to the positive x axis. Vector B has magnitude 12.3 and acts at an angle of 71.3 degrees with respect to the positive x axis. Vector C has magnitude 48.3 and acts at an angle of 147.7 degrees with respect to the positive x axis. Vector D has magnitude 11.0 and acts at an angle of 283.3 degrees with respect to the positive x axis.

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?

Express the magnitude to three significant figures. Express the angle to one decimal place, measured counterclockwise from the positivex axis. Separate your answers by a comma.

I am keep finding 36.626 and theta is 120.29 but it still says i am wrong can you please help me?? Thanks!

Explanation / Answer

A = 21.5 (cos13.1i + sin13.1j) = 20.94i + 4.87j

B = 12.3 (cos71.3i + sin71.3j) = 3.94i + 11.65j

C = 48.3 (cos147.7i + sin147.7j) = -40.83i + 25.81j

D = 11(cos283.3i + sin283.3j) = 2.53i -10.70j

R = A + B + C + D = -13.42i + 31.62j

magnitude = sqrt(13.42^2 + 31.62^2) = 34.35

direction = 180 - tan^-1(31.63/13.42) = 113 deg

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