Final answer:
The speed of the child at the bottom of the swing is approximately 6.26 m/s.
Step-by-step explanation:
To determine the speed (v) of the child at the bottom of the swing, we can use the concept of conservation of mechanical energy. At the highest point of the swing, all the potential energy is converted into kinetic energy. At the bottom of the swing, all the kinetic energy is converted into potential energy.
The potential energy at the highest point is given by:
PE = m * g * h
Where m is the mass of the child (20 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height from the center of mass to the highest point (2 m).
The kinetic energy at the bottom of the swing is given by:
KE = 1/2 * m * v²
Where v is the speed at the bottom of the swing.
Since we know that the potential energy at the highest point is equal to the kinetic energy at the bottom of the swing, we can set up the equation:
m * g * h = 1/2 * m * v²
Plugging in the given values, we get:
20 kg * 9.8 m/s² * 2 m = 1/2 * 20 kg * v²
Solving for v, we find that the speed at the bottom of the swing is approximately 6.26 m/s.