# The bicycle wheel has a radius of 40 m. Determine the speed of the cyclist if the wheel makes 120 revolutions per minute.

R = 40 m.

N = 120.

t = 1 min = 60 s.

V -?

The speed of movement V is the ratio of the traversed path S to the time of its passage t: V = S / t.

For 1 full revolution, the wheel point travels a distance equal to the circumference L of the radius R.

The length of the circle L is found by the formula: L = 2 * P * R, where P is the number pi.

During the time t, the wheel makes N revolutions, so whatever point of the wheel passes the distance S = N * L = N * 2 * P * R.

The bike speed V will be determined by the formula: V = N * 2 * P * R / t.

V = 120 * 2 * 3.14 * 40 m / 60 s = 502.4 m / s.

Answer: the speed of the cyclist is V = 502.4 m / s.

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