Answer to Question #225816 in Physics for Gelo

Question

Jerom is a veteran porter of Mountain Knot City and tasked to recover lost cargo which is surrounded by BTs. To be able locate the lost cargo and avoid BTs encounter, he must leave the city and follow the given direction carefully: A=10m, 60 degree north of east, B= 15 m, 30 degree west of north, and C= 5m, southward. Calculate the magnitude and direction of the resultant vector of Jerom. Use analytical method for your solution and include graph with scaling for dimensional analysis.

Answer 1

The resultant vector is

$$\vec D=\vec D_A+\vec D_B+\vec D_C,\\\space\\ \vec D=[10(i\cos60°+j\sin60°]+\\+[15(-i\sin30°+j\cos30­°]+[5(-j)]=\\ =-2.5i+16.7j,\\ |\vec D|=\sqrt{(-2.5)^2+(16.7)^2}=16.9\text{ m}.\\ \theta=\arctan\frac{16.7}{2.5}=81°\text{ N of E}.$$