A 20 kg child is on a swing that hangs from 2.4-m-long chains. part a what is her maximum speed if she swings out to a 44 ∘ angle?

Answer;

= 3.63 m/s

Explanation; The speed reaches its maximum V when the swing arrives at its vertical position. At that very moment its kinetic energy is mV^2/2. In the initial position the potential energy is mgL (1-cosA), where L is the length, and A is the maximum angle. Considering that the potential energy is zero in the vertical position. Conservation of energy requires that;

mV^2/2=mgL (1-cosA)

Thus;

V=sqrt[ (2gL (1-cosA) ]

= √[2 * 9.8 * 2.4 * (1 - cos 44) ]

= √ 13.202

= 3.63 m/s