Question

I A runner is training for an upcoming marathon by running around a 100-m-diameter circular track at constant speed. Let a coordinate system have its origin at the center of the circle with the -axis pointing east and the -axis north. The runner starts at and runs \(2.5\) times around the track in a clockwise direction. What is his displacement vector? Give your answer as a magnitude and direction.

Short answer

The displacement of runner is $100\text{m}$ west .

Step-by-step solution

Step .1. Given Information.

Displacement is the shortest path covered by particle, whose direction is in initial position to final position.

Total displacement covered by runner is equal to the diameter of circular track.

Step.2. Explanation.

Consider the following figure

From the above figure runner start at point $(50\text{m},0)$and runs $2.5$ times around the track in clockwise and ends up at the point $(-50\text{m},0)$.

The diameter of circular track is $100\text{m}$.

Therefore, the displacement of runner is$100\text{m}$ west .