A carnival swing is fixed on the end of an 7.6-m-long beam. If the swing and beam sweep through an angle of 130°, what is the distance through which the riders move?
To find the distance through which the riders move, we need to find the length of the arc of the swing's circular motion.
The distance along the circumference of a circle is equal to the product of the central angle (in radians) and the radius of the circle. Since the swing and beam sweep through an angle of 130°, we need to convert it to radians first.
To convert degrees to radians, we use the formula: radians = degrees × π / 180.
So, converting 130° to radians:
radians = 130° × π / 180
radians ≈ 2.2689 radians.
Given that the beam's length is 7.6 meters, the radius of the circular motion is 7.6 meters.
Now, we can find the length of the arc using the formula: arc length = radius × central angle.
arc length = 7.6 meters × 2.2689 radians ≈ 17.29 meters.
Therefore, the distance through which the riders move is approximately 17.29 meters.