Answer to Question #243415 in Math for Jaha

Question

F1 = 40N, 30º SE; F2 = 25N, 40º NW; and F3 = 30N, 50º NE, what is the resultant vector R?

Answer 1

$$F_1=(40\sin(180\degree-30\degree), 40\cos(180\degree-30\degree))$$

$$F_2=(25\sin(-40\degree), 25\cos(-40\degree))$$

$$F_3=(30\sin(50\degree), 30\cos(50\degree))$$

$$R=F_1+F_2+F_3$$

$$=(40\sin(150\degree)-25\sin(40\degree)+30\sin(50\degree),$$

$$40\cos(150\degree)-\cos(40\degree)+30\cos(50\degree))$$

$$\approx(26.911643, -34.508499)$$

$$|R|=\sqrt{(26.911643)^2+(-34.508499)^2}$$

$$=43.76\ N$$

$$\tan \theta=\dfrac{-34.508499}{26.911643}$$

$$\theta=-52.05\degree$$

$$R = 43.76\ N, 37.95º SE$$