Answer to Question #282408 in Physics for Charles

Question

Find the resultant of the following

vectors.

A = 30 m at 30° with the x-axis

B = 20 m at 120° with the x-axis

C = 10 m at 225° with the x-axis

Answer 1

Find the components of the vectors:

$$A_x = 30\cos30°,\\ B_x = 20\cos120°,\\ C_x = 10\cos225°,\\ R_x=A_x+B_x+C_x=8.9\text{ m}.\\\space\\ A_y = 30\sin30°,\\ B_y = 20\sin120°,\\ C_y = 10\sin225°,\\ R_y=A_y+B_y+C_y=25\text{ m}.\\\space\\ R=\sqrt{R_x^2+R_y^2}=27\text{ m},\\\space\\ \theta=\arctan\frac{R_y}{R_x}=70°.$$