Answer to Question #138974 in Physics for April Rose Besin

Question

Given are the vectors A = 30 N 45 N of W and B = 45 N 75 S of E. Determine a) their resultant and in Newtons b) What will be their direction(angle)?

Answer 1

a)

$$R_x=A_x+B_x=-30\cos{45}+45\cos{75}=-9.57\ N$$

$$R_y=A_y+B_y=30\sin{45}-45\sin{75}=-22.25\ N$$

$$R=\sqrt{9.57^2+22.25^2}=24.2\ N$$

b)

$$\theta=\arctan{\frac{22.25}{9.57}}=66.7\degree\text{ S of W}$$