Question

A bus leaves the terminal 208 degrees traveling 65 km turned W at 80 km then 60 degrees for 100 km. How far is the bus from the terminal and in what direction?

Answer 1

Calculate the displacement along WE direction:

$$D_{WE}=65\text{ cos}(208º-180º)+80+100\text{ cos}60º=\\=187\text{ km}.$$

Calculate the displacement along NS direction:

$$D_{NS}=65\text{sin}(208º-180º)+0-100\text{sin}60º=\\ =56\text{ km}.$$

The total displacement:

$$D=\sqrt{D^2_{WE}+D^2_{NS}}=195\text{ km}.$$

The angle above W-axis:

$$\theta=\text{atan}\frac{D_{NS}}{D_{WE}}=17º.$$