Answer to Question #130313 in Physics for Alan

Question

Add the given vectors, both parallelogram method and component method. Use the scale
1cm:10 m in the parallelogram method. Compare the magnitude of the resultant from the two
methods by solving for the percentage difference (%D) using the formula given on the concept
notes.
A = 130 m, North
B = 60 m, 35° S of E
C = 85 m, 50° W of S

Answer 1

Now add using the component method. Find x- and y-components of every vector, sum up each x-components and then all y-components and find the resultant by Pythagorean theorem:

$$A_x=0\\ A_y=130\\ B_x=-60\text{ cos}35°=-49\\ B_y=-60\text{ sin}35°=-34\\ C_x=85\text{ sin}50°=65\\ C_y=-85\text{ cos}50°=-55\\ R_x=A_x+B_x+C_x=0-49+65=16\\ R_y=A_y+B_y+C_y=130-34-55=41\\ R=\sqrt{R_x^2+R_y^2}=\sqrt{16^2+41^2} =44\\ \theta_R=\text{atan}\frac{R_y}{R_x}=69°\text{ N of W}.$$

According to our image, the % difference in magnitude is around 30%.