A quarterback back pedals 2.2 meters southward and then runs 6.8 meters northward.

Question

What is the magnitude and direction of the displacement?

Answer 1

Let (0,0) be the (x,y) coordinates at the start. After he back-pedals South, he is at (0,-2.2). From there he runs 6.8 m North, so y = -2.2 + 6.8 = 4.6 and he ends at (0,4.6). Displacement is the change in position from initial to final, x_f - x_i = 0, y_f - y_i = 4.6 - 0 = +4.6. His displacement has a magnitude of 4.6 m and a direction of North.