Final answer:
The potential energy of a 25.0-kg child at the highest point of a swing, which is 2.00 m above the child's center of mass, is calculated to be 490.5 Joules using the gravitational potential energy formula.
Step-by-step explanation:
To calculate the potential energy of a 25.0-kg child at the highest point of a swing, we use the formula for gravitational potential energy (PE = mgh), where m is mass, g is the acceleration due to gravity (9.81 m/s² by convention, but sometimes approximated to 10 m/s² for simplicity in calculations), and h is the height above the reference point. In this scenario, the swing is 2.00 meters above the child's center of mass when the child is at the highest point.
Using the provided values, the potential energy at the highest point can be calculated as follows:
PE = mgh = (25.0 kg) × (9.81 m/s²) × (2.00 m) = 490.5 Joules.
Therefore, the child has 490.5 Joules of potential energy at the highest point.