A 29.0-kg child on a 3.00-m-long swing is released from rest when the ropes of the swing make an angle of 25.0° with the vertical. (a) Neglecting friction, find the child's speed at the lowest position.

v = 2.348 m/s

Explanation:

Let:

h be the height of the child above the swing's low point,

v be the speed at the low point.

When the ropes make angle 3

25 deg. with the vertical:

h = 3.00(1 - cos(25)).

Equating potential energy at the high point to kinetic energy at the low point:

29.0 * 9.81 * 3.00(1 - cos(25)) = 29.0v^2 / 2

79.96 =29.0v^2 / 2

v = 2.348 m/s