Compute the x - and y -components of the vectors and in Fig. E1.24.
Solution 31E If a vector A making an angle with the positive x axis, the we can write that, the x component of the vector is A = |A|cos x And y component of the vector is A y |A|sin Now from the given figure, first we have to calculate the angle of the vector making with the positive x axis and then we can calculate the components. The figure is: Step 1 (vector A). a) vector A is parallel to the negative y axis, hence the angle , that vector A is making with the positive x axis is = 270° The magnitude of the vector is |A| = 8.00 m So the x component of the vector ix A = |A|cos = (8.00 m)cos270° = 0 The y component of the vector isyA = (8.00 m)sin270° = 8.00 m Step 2 (vector B ) The angle of vector B with the positive x axis is = 90.0° 30.0° = 60.0° And the magnitude is|B| = 15.0 m B = (15.0 m)cos60° = 7.50 m Hence the x component is x The y component is By= (15.0 m)sin60° = 13.0 m