Answer:
The length of the arc travelled by the swing is approximately 3.77 m
Step-by-step explanation:
The given parameters of the swing are;
The swing base height of the swing above the ground = 72 cm
The swing base height above the when the swing travels an angle of 60° = 252 cm
Therefore we have;
r × cos(60°) = r - 180
180 = r - r × cos(60°)
r = 180/(1 - cos(60°)) = 360
r = 360 cm
The length of the arc travelled by the swing in meters, [tex]l_{arc}[/tex] is given as follows;
[tex]l_{arc} = \dfrac{\theta}{360 ^{\circ}} \times \pi \times 2\times r[/tex]
Therefore;
[tex]l_{arc} = \dfrac{60^{\circ}}{360 ^{\circ}} \times \pi \times 2\times360 = \dfrac{1}{6} \times \pi \times 720 = 120 \cdot \pi[/tex]
The length of the arc travelled by the swing, [tex]l_{arc}[/tex] = 120·π cm
∴ The length of the arc travelled by the swing, [tex]l_{arc}[/tex] = 1.2·π m ≈ 3.77 m
