Showing that energy of a falling object remains constant

[MadmanMurray]

I got this question on a sample test but I don't know how they want me to answer it
Q.) Show that for a falling body, the total amount of energy is constant at any point
I suppose I could state the potential energy then draw a graph of how the potential energy is converted into velocity. Is that what they mean?

 

[rl.bhat]

Consider the starting point, end point and anyone point in between them. Then find potential energy, kinetic energy at these point and find the total energy. Show the it remains constant.

 

[thomate1]

Yes, that is one way to show that the energy of a falling object remains constant. Another way to explain this concept is through the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted from one form to another. In the case of a falling object, the potential energy (due to its position in a gravitational field) is converted into kinetic energy (due to its motion) as it falls. This conversion from potential to kinetic energy is what allows the object to maintain a constant total energy throughout its fall. Additionally, the work-energy theorem can be used to mathematically prove that the total energy of a falling object remains constant at any point. Overall, there are multiple ways to demonstrate and explain the concept of constant energy in a falling object, and it is important to understand and apply these principles in scientific studies and experiments.