Answer
a. Vsumx = 24.03 units
Vsumy = 11.63 units
b. The sum vector has magnitude of 26.7 units and points at an angle of 25.8$^o$.
Work Step by Step
a. Use equations 3.3a and 3.3b to find the x and y components. Vector B points at 124 degrees and vector C points at 270 degrees from the positive x-axis.
Vector A = (38.85, 20.66)
Vector B = (-14.82, 21.97)
Vector C = (0, -31)
The x-component of the resultant/sum is the sum of the x-components.
Vsumx = 24.03 units
The y-component of the sum is the sum of the y-components.
Vsumy = 11.63 units
b. The components are obtained. Use the Pythagorean theorem 3.4a to find the magnitude of the overall vector, and the definition of tangent, equation 3.4b, to find the angle. The vector has positive x-component and positive y-component, and points up and to the right.
The sum vector has magnitude of 26.7 units and points at an angle of 25.8$^o$.
