The distance through which the rider at the end of the beam moves is;
L = 15.5 m
We are told that the beam on which the carnival ride is fixed is 12.6m in length.
Since the seat is at the end of the beam with the other end pivoted and the beam sweeps through an angle of 141°, then we can say that the radius of this arc formed by the swing is;
Radius; r = 12.6 m
Also, θ = 141°
The distance through which the driver moves will be the length of the arc formed by the beam at angle of 141°.
Formula for length of arc is given as;
L = 2πr(θ/360)
Plugging in the relevant values gives;
L = 2π × 12.6 × 141/360
L = 15.5 m
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