Question

Find the magnitude and direction of R=A+B, given that A has magnitude 4 and it has an angle of30° above the positive x-axis and B has magnitude 2 and it has an angle of55° above the positive x-axis

Answer 1

$$R_x=4cos30^{\circ}+2cos55^{\circ}=4.61,$$ $$R_y=4sin30^{\circ}+2sin55^{\circ}=3.64.$$

The resultant of the sum of two vectors can be found from the Pythagorean theorem:

$$R=\sqrt{R_x^2+R_y^2}=\sqrt{(4.61)^2+(3.64)^2}=5.87$$

We can find the angle as follows:

$$\theta=cos^{-1}(\dfrac{R_x}{R})=cos^{-1}(\dfrac{4.61}{5.87})=38.27^{\circ}.$$

The resultant R has magnitude 5.87 and angle of $38.27^{\circ}$ above the positive x-axis.