Answer to Question #253918 in Mechanics | Relativity for Kyla

Question

Using component method of getting the resultant of vectors, find the resultant of the following vectors: 7N along the positive x axis, 5N making an angle of 35o with the x axis, and 3N, 36o South of West.

Answer 1

Determine the corresponding components of the resultant vector:

$$A_x=7\text{ N},\\ A_y=0,\\ B_x=5\cos35°=4.1\text{ N},\\ B_y=5\sin35°=2.9\text{ N},\\ C_x=-3\cos36°=-2.4\text{ N},\\ C_y=-3\sin36°=-1.8\text{ N}.\\\space\\ R_x=A_x+B_x+C_x=9.5\text{ N},\\ R_y=A_y+B_y+C_y=1.1\text{ N},\\ R=\sqrt{R_x^2+R_y^2}=9.6\text{ N},\\\space\\ \theta=\arctan\frac{R_y}{R_x}=6.6°\text{ above x-axis}.$$