What is the resultant vectro R obtained by adding vectors C and Dc What is the r

Question

What is the resultant vectro R obtained by adding vectors C and Dc What is the resultant vectro R obtained by adding vectors C and Dc What is the resultant vectro R obtained by adding vectors C and Dc Geometric and Component Vector Addition Learning Goal: To use geometric and component addition of vectors. Four vectors A, B. C, and D are shown (not to scale). Vector A has magnitude 18.3 and acts at an angle of 14.5 degrees with respect to the positive x axis. Vector B has magnitude 12.1 and acts at an angle of 74.5 degrees with respect to the positive x axis. Vector C has magnitude 38.1 and acts at an angle of 141.5 degrees with respect to the positive x axis. Vector D has magnitude 14.0 and acts at an angle of 282.1 degrees with respect to the positive x axis. (Figure 1) Figure 1 of 1>

Explanation / Answer

To find the Resultant vector R obtained by adding C and D; we carry out following component wise addition:

Vector C components: X-component = 38.1*cos(141.5 degree) = -29.817 = Cx ;

                                 Y-component = 38.1*sin(141.5 degree) = 23.717 = Cy ;

Vector D components: X-component = 14*cos(282.1 degree) = 2.934 = Dx ;

                                 Y-component = 14*sin(282.1 degree) = -13.688 = Dy ;

Now Resultant vector R's components :

Rx = Cx + Dx = -29.817 + 2.934 = -26.883

Ry = Cy + Dy = 23.717 + (-13.688) = 10.029;

Writing magnitude and angle for vector R, magnitude = ( Rx^2 + Ry^2 )^ (1/2) = 28.69;

                                                              Angle with positive x-axis = 159.54 degree .

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