Question

An aeroplane flies from origin to city located 175 kilometre 30 degree northof East next it flies 153 kilometre 20 degree centigrade west of north to city B.finally it flies 195 kilometre due West to city C find the total displacement

Answer 1

$$\bold{s_1}=(-175\cos{30},175\sin{30})=(-151.6,87.5)km$$

$$\bold{s_2}=(153\sin{20},153\cos{20})=(52.3,143.8)km$$

$$\bold{s_3}=(195,0)km$$

$$s_x=195+52.3-151.6=95.7\ km$$

$$s_y=87.5+143.8=231.3\ km$$

The magnitude:

$$s=\sqrt{95.7^2+231.3^2}=250\ km$$

The direction:

$$\theta=\arctan{\frac{95.7}{231.3}}=22.5\degree W\ of\ N$$