What is the final velocity of a hoop that rolls without slipping down a 5.00-m-high hill, starting from rest?

In every natural phenomena existing, there are three law of conservations that must always be follows: the Law of Conservation of Mass, Energy and Momentum. Let's focus particularly in the conservation of energy. Energy is neither created nor destroyed, it just transferred from one form to another. With that being said, the energy from the hoop from start to finish does not change. When ti was on top of the hill, it possesses potential energy. As it moves down the hill, potential energy is transformed to kinetic energy. So, the conservation is presented in this equation:

Potential energy = Kinetic energy

mgh = 1/2*mv²

where

m is the mass of the hoop

g is the acceleration due to gravity equal to 9.81 m/s²

h is the height

v is the final velocity

Simplifying the equation, we cancel out m at both sides:

gh = 1/2*v²

Substituting the values:

(9.81) (5) = 1/2*v²

v² = 98.1

v = √98.1

v = 9.9 m/s