Question

A swing base is 72 cm above the ground as shown in figure. When it travels through an angle of 60∘ from its mean position, swing base comes at 252 cm above the ground. What is the length of the arc travelled by the swing in meters?​

Answer 1

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, $l_{arc}$ is given as follows;

$l_{arc} = \dfrac{\theta}{360 ^{\circ}} \times \pi \times 2\times r$

Therefore;

$l_{arc} = \dfrac{60^{\circ}}{360 ^{\circ}} \times \pi \times 2\times360 = \dfrac{1}{6} \times \pi \times 720 = 120 \cdot \pi$

The length of the arc travelled by the swing, $l_{arc}$ = 120·π cm

∴ The length of the arc travelled by the swing, $l_{arc}$ = 1.2·π m ≈ 3.77 m