Two athletes are competing on the ski track. The speed modulus of the first is 8 m / s, and of the second, 5 m / s.

Two athletes are competing on the ski track. The speed modulus of the first is 8 m / s, and of the second, 5 m / s. What was the distance between them at the initial moment of time if the first skier caught up with the second one after 180 s?

V1 = 8 m / s.

V2 = 5 m / s.

t = 180 s.

S -?

With a uniform rectilinear movement, the path traversed by the athlete is determined by the formula: S1 = V1 * t, S2 = V2 * t, where V1, V2 are the speeds of their movement, t is the time of movement.

Let us represent the distance traveled by the first sportsman S1 by the expression: S1 = S + S2, where S is the distance between the sportsmen at the start.

V1 * t = S + V2 * t.

At the initial moment of time, the distance between the athletes will be determined by the formula: S = V1 * t – V2 * t = (V1 – V2) * t.

S = (8 m / s – 5 m / s) * 180 s = 540 m.

Answer: at the initial moment of time, the distance between the athletes was S = 540 m.