Answer to Question #179750 in Physics for Meme Bow

Question

Find the magnitude and direction of the resultant of the following vectors using Laws of Sines and Cosines:10N, E 50°N and 8 N, W 10°S. Use scale drawings.

Answer 1

According to law of cosines find the magnitude of the resultant green vector:

$$R^2=A^2+B^2-2AB\cos\theta,\\\space\\ R=\sqrt{10^2+8^2-2·10·8\cos120°}=15.6\text{ N}.$$

According to law of sines, find angle α:

$$\frac{\sin\alpha}{8}=\frac{\sin120°}{15.6},\\\space\\ \alpha=\arcsin\bigg(\frac{8}{15.6}·\sin120°\bigg)=26.4°.$$

Thus, the direction of R is

$$\delta=90°-40°-26.4°=23.6°\text{ E of N}.$$