Answer to Question #283575 in Physics for Harrisonfaith

Question

Find graphically and analytically the resultant of the following displacements A 10m northwest B 20m30° north of east C 35m due south

Answer 1

$A_N=10\cos45°=7.1\text{ m}.\\ A_E=-10\sin45°=-7.1\text{ m}.\\ B_N=20\sin30°=10\text{ m}.\\ B_E=20\cos30=17\text{ m}.\\ C_N=-35\text{ m},\\ C_E=0.\\\space\\ R_N=A_N+B_N+C_N=-17.9\text{ m},\\ R_E=A_E+B_E+C_E=9.9\text{ m},\\ R=\sqrt{R_N^2+R_E^2}=20\text{ m}.\\\space\\ \theta=\arctan\dfrac{R_E}{R_N}=28.9°\text{ E of S}.$