Question

what is the resultant displacement if a man jogs 120m, east, and then walks 50m due south?

Answer 1

We can find the magnitude of the resultant displacement from the Pythagorean theorem:

$$d_{res}=\sqrt{d_x^2+d_y^2}=\sqrt{(120\ m)^2+(-50\ m)^2}=130\ m.$$

We can find the direction of the resultant displacement from the geometry:

$$\theta=tan^{-1}(\dfrac{d_y}{d_x}),$$ $$\theta=tan^{-1}(\dfrac{-50\ m}{120\ m})=22.6^{\circ}\ S\ of\ E.$$