Let the center of the circle be O, the farthest points on both sides are A and B, the intersection point in the middle is C, and the intersection point between the vertical line and the arc in the middle is D.

Because the rope of the swing is 3m long, the pedal is 0.5m off the ground at rest, and the pedal at the top of the swing is 2m off the ground, therefore:

OC = OD-CD = 3-(2-0.5) = 1.5m。

Looking at the right triangle OAC, OC=OA/2, we can get the angle AOC=60 degrees, that is, the angle AOB= 120 degrees.

That is, the arc of the swing is 1/3 circle.

The answer = 2× ∈× r/3 = 2× 3.14× 3/3 = 6.18m.

Next time you ask a geometry question, you'd better mark the key points with ABCD or something.