Question

Two campers in a national park hike from their cabin to the same spot on a lake, each taking a different path, as illustrated below. The total distance traveled along Path 1 is 7.5km, and that along Path 2 is 8.2km. What is the final displacement of each camper?

Short answer

The displacement of both the campers is the same—5.0 Km. 40° north-east.

Step-by-step solution

Displacement

Displacement is defined as the shortest path between an initial and final position. It is a vector quantity.

If $\stackrel{\mathbf{\rightharpoonup }}{{\mathbf{r}}_{\mathbf{A}}}$and $\stackrel{\rightharpoonup }{r_B}$are the position vectors of initial and final points of a particle, then the displacement of the particle is${\stackrel{\mathbf{\rightharpoonup }}{\mathbf{r}}}_{\mathbf{A}\mathbf{B}}\mathbf{=}{\stackrel{\mathbf{\rightharpoonup }}{\mathbf{r}}}_{\mathbf{B}}\mathbf{-}{\stackrel{\mathbf{\rightharpoonup }}{\mathbf{r}}}_{\mathbf{A}}$

Displacement of the campers

A displacement is defined as the change in the final and initial positions of a body. It does not depend on the path followed by a moving body; it simply depends on the final and initial positions of a body. The magnitude of displacement is given by the length of the straight line joining the initial and final positions of the moving body.

We see that both the campers start from the same point and finish their journey at the same position. Therefore, the displacement of both the campers is the same—5.0 Km. 40° north-east.