A 20 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 45° angle?

The solution for this problem is:

Remember that this doesn’t depend on the mass of the child.

E = T + U = constant

E (maximum height) = T + U = U = mgh = mg[r - r· cos (Θ) ]

E (bottom height) = T + U = T = ½mv² = mg[r - r · cos (Θ) ]

v² = 2g[r - r · cos (Θ) ]

v = √ (2g[r-r·cos (Θ) ])

= √ (2 (9.8) [3 - 3 · cos (45°) ])

= 4.15 m/s or 15 kph