An athlete, moving at a constant absolute speed, runs through the stadium for 3.5 laps.

An athlete, moving at a constant absolute speed, runs through the stadium for 3.5 laps. How many times is the movement module and the athlete’s path different?

n = 3.5.

L / S -?

The distance traveled L is the length of the line that the athlete describes when moving.

Since the athlete makes n circles, he goes the path L = n * L1, where L1 is the length of one full circle.

The length of the circle is determined by the formula: L1 = 2 * P * R, where P is the number pi, R is the radius of the circle.

L = n * 2 * P * R.

The movement of the athlete S is called the vector that connects the starting and ending position of the body.

Since the athlete makes n = 3.5 rotations, he stops on the opposite side of the circle from which he started. Moving S will be the diameter of the circle: S = 2 * R.

L / S = n * 2 * P * R / 2 * R = 2 * n * P.

L / S = 2 * 3.5 * 3.14 = 22.

Answer: the athlete’s path is 22 times longer than his movement: L / S = 22.