Question

Vector C has a magnitude 28.2m and is in the direction of the negative y axis. Vectors A and B are at angles alpha = 42.4 degrees and Beta = 28.7 degrees up from the x axis respectively. If the vector sum A + B + C =0, what are the magnitudes of A and B?.

Answer 1

Taking two components of Vector A, Ax along x axis and Ay along y-axis

Ax = Acos(alpha) and Ay = Asin(alpha)

Since alpha = 42.4 => Ax = 0.738*A and Ay = 0.674*A

similarly, Bx = -Bcos(beta) and By = Bsin(beta)

Since Beta = 28.7 => Bx = -0.877*B and By = 0.48*B

here A and B are magnitudes of respective vectors

given Vector sum of 3 vectors = 0

=> net x-component = 0 => Ax+Bx+Cx = 0

=> A*0.738-B*0.877+0 = 0

A = 1.188*B

Also, Ay+By+Cy = 0

=>A*0.674+B*0.48 -28.2 = 0

=>B(1.188*0.674+0.48) = 28.2

Solving these two equations

=>B = 22.019 m

=>A = 26.158 m

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