One of the standard tracks used in athletic events is a 400m loop. This track consists of two straight sections
joined by semi-circular sections and one lap of the track in the inside lane is exactly 400 m.
(a) What is the displacement of a runner in the inside lane when they finish a 400 m race? Is the displacement
of the runner in the outside lane the same?
To find the displacement of a runner in the inside lane when they finish a 400m race, we need to consider the geometry of the track.
The track consists of two straight sections joined by semi-circular sections. The inside lane, being closest to the center of the track, will be shorter than the outside lane.
To determine the displacement of the runner in the inside lane, we first need to calculate the circumference of the semi-circle.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. In this case, the radius of the semi-circle is half of the diameter of the track, which is 400m.
So, the circumference of the semi-circle is C = 2π * 200m = 400πm.
Next, we need to calculate the distance covered by the runner on the straight sections. Since the inside lane is exactly 400m, the runner will cover the entire distance on the straight sections.
Therefore, the displacement of the runner in the inside lane will be the sum of the distances covered in the straight sections, which is 400m.
On the other hand, the runner in the outside lane will have to cover a longer distance due to the wider radius of the track. Therefore, their displacement will be greater than 400m.
In summary, the displacement of a runner in the inside lane is 400m, whereas the displacement of a runner in the outside lane will be greater than 400m.
One of the standard tracks used in athletic events is a 400m loop. This track consists of two straight sections
joined by semi-circular sections and one lap of the track in the inside lane is exactly 400 m.
(a) What is the displacement of a runner in the inside lane when they finish a 400 m race? Is the displacement
of the runner in the outside lane the same?