Answer to Question #242381 in Electricity and Magnetism for Baloch

Question

A commuter airplane takes the route shown in Figure 3.20. First, it flies from the origin of the coordinate system shown to city A, located 175 km in a direction 30.0° north of east. Next, it flies 153 km 20.0° west of north to city B. Finally, it flies 195 km due west to city C. After landing in city C, the pilot wishes to return to the origin along a straight line. What are the components of the vector representing this displacement? What should the heading of the plane be?

Answer 1

The components of the vector are

$$R_E=-(175\cos30-153\sin20-195)=\\= 95.8\text{ km East}.\\\space\\ R_S=175\sin30+153\cos20=231\text{ km South}.\\\space\\ \theta=\arctan\frac{R_E}{R_S}=22.5°\text{E of S}.$$