Question

An airplane takes the following route to reach the city C.

First it flies from the origin of the coordinate system to city A located 175 km in a direction 30° north of

east.

Next it flies 153 km 20° west of north to city B. Finally it flies 195 km due west to city C.

NOTE: Angle should be taken from positive x-axis.

(a) Find the location of city C relative to the origin.

(b) Also draw the graph.

Consider same problem in question 1, after landing in city C, the pilot wishes to return to the origin

along a single straight line. What are the components of the vector representing this displacement?

What should the heading of the plane be?

Answer 1

$$x=-175\cos{30}+153\sin{20}+195=95.8\ km\\ y=175\sin{30}+153\cos{20}=231.3\ km\\s=\sqrt{95.8^2+231.3^2}=250\ km\\\theta=\arctan{\frac{95.8}{231.3}}=22.5\degree\text{ W of N}$$