A carnival swing is fixed on the end of an 8 m long beam. If the swing and the beam sweep through an angle of 120 degrees, what is the distance through which the riders move?
The distance through which the riders move is equal to the length of the arc formed by their path, which can be calculated with the formula:
Arc length = radius × angle (in radians)
First, we need to convert the angle from degrees to radians. To do that, we use the formula:
radians = degrees * π / 180
So:
radians = 120 * π / 180 = (2/3)π
Now we can calculate the arc length:
Arc length = 8m * (2/3)π = 16π/3 meters ≈ 16.755 meters
Therefore, the riders move approximately 16.755 meters along their path.