A20 kg child is on a swing that hangs from 3.0-m-long chains. what is her maximum speed if she swings out to a 49 ∘ angle?

L = length of the chain = 3 m

θ = angle with the vertical = 49 deg

h = height gained

In triangle ABD

Cosθ = AB/AD

Cosθ = AB/L

AB = L Cosθ

BC = AC - AB = L - L Cosθ

so h =  L - L Cosθ

inserting the values

h =  (3) - (3) Cos49 = 1.032 m

v = maximum speed at the bottom of the swing

Using conservation of energy

kinetic energy at the bottom of the swing = potential energy at the maximum height

(0.5) m v² = mg h

v = sqrt(2gh)

v = sqrt(2 x 9.8 x 1.032)

v = 4.5 m/s

12000j is work done

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees.