Question

Bryan is walking alone in the Madrid park going to the superstore. He is travelling from Madrid park 150m, 30° West of North, then 200m, 50° East of North, and 250m North. What is the displacement of the problem.

Answer 1

Draw his path:

Find x- and y-components of the vectors:

$$A_x=-150\text{sin}30°=-75\text{ m}.\\ A_y=150\text{cos}30°=130\text{ m}.\\ B_x=200\text{sin}50°=153\text{ m}.\\ B_y=200\text{ cos}50°=129\text{ m}.\\ C_x=0.\\ C_y=250\text{ m}.$$

The components of the green displacement:

$$D_x=A_x+B_x+C_x=78\text{ m}.\\ D_y=A_y+B_y+C_y=509\text{ m}.$$

The displacement is

$$D=\sqrt{D_x^2+D_y^2}=515\text{ m}.$$