Answer to Question #188987 in Physics for Ayan Khan

Question

Find the resultant if the following forces acts on a body

12N along x-axis

8N along y-axis

4N at 30° along x-axis

Answer 1

Find the components:

$$F_{1x}=12\text{ N},\\ F_{1y}=0,\\ F_{2x}=0,\\ F_{2y}=8\text{ N},\\ F_{3x}=4\cos30°=3.46\text{ N},\\ F_{3y}=4\sin30°=2\text{ N}.\\$$

The resultant:

$$R_x=F_{1x}+F_{2x}+F_{3x}=15.46\text{ N},\\ R_y=F_{1y}+F_{2y}+F_{3y}=10\text{ N},\\ R=\sqrt{R_x^2+R_y^2}=18.41\text{ N},\\\space\\ \theta_R=\arctan\frac{R_y}{R_x}=32.9°.$$