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Kinetic energy is one of the fundamental forms of energy associated with the motion of an object. Whenever an object moves, it possesses kinetic energy, which depends on two main factors:

• Mass of the object (\(m\)
• Velocity of the object (\(v\)

The formula for calculating kinetic energy (\(KE\)) is:\[ KE = \frac{1}{2}mv^2 \]Initially, when the rock is released from a height of 20 meters, its velocity is zero because it is at rest. This means its initial kinetic energy is zero. As the rock falls, it gains speed, and its kinetic energy increases. At a height of 10 meters, the rock has some kinetic energy because of its increasing velocity. By the time it reaches the ground, the kinetic energy reaches a maximum due to its maximum velocity at this point.
Ultimately, kinetic energy reflects how much work an object in motion can potentially perform due to its speed and mass.

Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. It is directly related to the height of the object relative to a reference point, often taken as the ground. The formula for calculating gravitational potential energy (\(PE\)) is:\[ PE = mgh \]where:

• \(m\) is the mass of the object
• \(g\) is the acceleration due to gravity, approximately 9.81 \(\text{m/s}^2\)
• \(h\) is the height above the reference point

At the start, when the rock is at 20 meters, it holds the maximum potential energy because it is as high as it gets, storing more energy due to its elevated position. As the rock descends to 10 meters and eventually to the ground, its potential energy decreases, because its height above the ground decreases. When the rock finally hits the ground, its potential energy becomes zero.

Mechanical energy is the sum of kinetic and gravitational potential energy that an object possesses. Due to the conservation of energy principle, if external forces like air resistance are negligible, the total mechanical energy remains constant throughout the motion. Mathematically, it can be expressed as:\[ TME = KE + PE \]For the rock falling from 20 meters, the total mechanical energy at each height should remain at 392.2 J, based on the conservation of energy law. Although the individual amounts of kinetic and potential energy change as the rock falls, their sum remains constant. At 20 meters, mechanical energy is entirely potential since kinetic energy is zero. As the rock descends to 10 meters, part of its mechanical energy converts into kinetic energy, while the rest remains as potential energy. Upon reaching the ground, all the potential energy is transformed into kinetic energy, maximizing the rock's kinetic energy while the total mechanical energy stays unchanged.