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Gravitational potential energy is a form of energy that an object possesses because of its position in a gravitational field. It's the energy that an object has due to its height above the ground.
The formula is given by \[ PE = -\frac{GMm}{R} \] where

• \( G \) is the gravitational constant,
• \( M \) is the mass of the planet,
• \( m \) is the mass of the object, and
• \( R \) is the radius of the planet.

When objects are moved from a distance to a closer point within the gravitational field, this energy can be converted to other forms of energy, such as kinetic energy. The negative sign in the formula indicates that gravitational potential energy is inversely related to the distance from the center of the planet.
This energy transformation is crucial when objects fall towards a planet, as it converts into kinetic energy, moving from potential to motion.

Kinetic energy is the energy of motion. When an object moves, it harnesses kinetic energy, which is calculated using the formula: \[ KE = \frac{1}{2} mv^2 \] Here,

• \( m \) is the mass of the object, and
• \( v \) is its speed.

In our gravitational problem, as the object falls, its gravitational potential energy decreases while its kinetic energy increases. This is due to the conservation of energy; the potential energy that the object loses is transformed into kinetic energy, causing the object to speed up. When the object finally hits the ground, all of its initial gravitational potential energy has been converted into kinetic energy. Understanding this concept helps us solve various physics problems involving motion and energy transformations, making it a key component of studying physics.

Physics problem solving involves using known principles to find unknown values, which is accomplished through systematic approaches like applying the law of energy conservation. The core idea here is the exchange between energies. When faced with a question like the initial exercise, start by identifying energy forms at the start and end of the object's journey.In our exercise, we learned that initially, the object has gravitational potential energy due to its height. As it falls, this is transformed into kinetic energy just before impact. This energy exchange can be handled with the conservation equation: \[\text{Total Energy Initial} = \text{Total Energy Final} \]
Follow steps like:

• Identifying known quantities and formulas,
• Substituting these into the energy conservation equation, and
• Solving algebraically for the unknowns.

This approach allows solving for quantities like speed at impact, ensuring robust understanding of energy transformations. This method underscores the beauty of physics—connecting concepts to observe how nature operates.