Question

1. Consider a circular track with a radius of 200 meters. A runner starts on the east side and runs around the track to a point diametrically opposite her starting point. What is the magnitude of her displacement? She then runs the rest of the way around the track to complete a full lap. What is the magnitude of her total displacement after she has returned to her starting point?

Answer 1

The magnitude of her displacement when at a point diametrically opposite her starting point is 400 meters

After she has returned to her starting point, the magnitude of her displacement is zero

Step-by-step explanation:

Displacement is a vector quantity defined as the length of the shortest path between the final and the initial points. In other words, displacement can be defined as the distance traveled in a straight line.

From the question,

The circular track has a radius of 200 meters.

The runner starts on the east side to a point diametrically opposite her starting point. The diametrically opposite point is the point at the opposite end of the diameter of the circle.

Hence, her displacement ( that is, the length of the shortest path between her final and her initial points) is the length of the diameter of the circle.

Diameter d, of a circle is given as twice the radius r, of the circle.

That is, d = 2r

Radius r, of the circular track is 200 meters

∴ d = 2r = 2 (200 meters)

d = 400 meters

Hence, her displacement when at a point diametrically opposite her starting point is 400 meters

Now, after she has returned to her starting point, the magnitude of her displacement is zero.

This is because, the length between her final point ( which is the same as her initial point) and her initial point in zero.