A carnival swing is fixed on the end of an 7.72-m-long beam. If the swing and beam sweep through an angle of 120°, what is the distance through which the riders move?
Question
A carnival swing is fixed on the end of an 7.72-m-long beam. If the swing and beam sweep through an angle of 120°, what is the distance through which the riders move?
Solution
The distance the riders move can be calculated using the formula for the length of an arc of a circle, which is given by:
Length = r * θ
where r is the radius of the circle (in this case, the length of the beam) and θ is the angle the arc sweeps through (in this case, the angle the swing and beam sweep through).
However, θ must be in radians for this formula to work. To convert from degrees to radians, we use the fact that 180° is equal to π radians. So,
120° = 120 * π / 180 = 2π / 3 radians
Now we can substitute r = 7.72 m and θ = 2π / 3 radians into the formula:
Length = 7.72 m * 2π / 3 = 16.14 m
So, the riders move through a distance of approximately 16.14 meters.
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