Answer to Question #265985 in Physics for Gayle

Question

Find the sum of the vector using the component method. Please show the solution.

(vec) A = 5m, 25°

(vec) B = 11m, 125°

(vec) C = 25m, 35°

Note:

(vec) R = (vec) A + (vec) B + (vec) C

Answer 1

Find the components:

$$A_x=5\cos25°=4.5\text{ m},\\ A_y=5\sin25°=2.11\text{ m}.\\ B_x=11\cos125°=-6.31\text{ m},\\ B_y=11\sin125°=9.01\text{ m}.\\ C_x=25\cos35°=20.4\text{ m},\\ C_y=25\sin35°=14.3\text{ m}.\\\space\\ R_x=A_x+B_x+C_x=18.6\text{ m},\\ R_y=A_y+B_y+C_y=25.4\text{ m}.\\\space\\ R=\sqrt{R_x^2+R_y^2}=27.9\text{ m}.\\\space\\ \theta=\arctan\frac{R_y}{R_x}=53.8°.$$