Study the scenario. A rock is thrown in the air with 1,000 J of energy. The isolated system consists of the rock, the person, and the Earth, ignoring air resistance. At some point on its path up, there is 900 J of kinetic energy in the system. Which choice best describes the amount and form of energy in this system when the rock is at this point?
There are more than 100 J of gravitational potential energy in the system because the rock is at some position relative to the ground, and the total energy must be more than 1,000 J. Some energy is gained during energy transformation.
There are slightly less than 100 J of gravitational potential energy in the system because the rock is at some position relative to the ground, and the total energy will be less than 1,000 J. Some energy is lost during transformation.
All of the energy is in the rock at this point in time is kinetic energy. There are 0 J of any other energy in the system because gravity is not pulling on it at this moment.
There are exactly 100 J of gravitational potential energy in the system because the rock is at some position relative to the ground. There must be a total of 1,000 J of energy in the system because energy is conserved.

There are exactly 100 J of gravitational potential energy in the system because the rock is at some position relative to the ground. There must be a total of 1,000 J of energy in the system because energy is conserved.

Explanation:

The law of conservation of energy states that energy can be interchanged into different forms, but the total amount of energy in an isolated system must always remain constant.

Here, we have an isolated system, consisting of a person, a stone, and the Earth. The rock is thrown in the air with a total energy of 1000 J. Since, the air resistance is ignored. Therefore, the only forms of energy at play here are Kinetic Energy and Potential Energy. So, according to law of conservation of energy:

Total Energy = Kinetic Energy + Potential Energy

At a point where the rock has 900 J of Kinetic Energy:

1000 J = 900 J + Potential Energy

Potential Energy = 1000 J - 900 J

Potential Energy = 100 J

Therefore, the best choice that describes the amount and form of energy at this point is:

There are exactly 100 J of gravitational potential energy in the system because the rock is at some position relative to the ground. There must be a total of 1,000 J of energy in the system because energy is conserved.