Velocity and Potential energy?

Question

If an object of mass 10.0Kg starts 5.0m above the ground what are the kinetic and potential energies at 2.5m above the ground? what is the velocity at this same height

Answer 1

Assuming we start with the object at rest.

Ignoring friction means that the initial energy is equal to the final energy. Starting the object at rest means that the initial KE is zero since it is not moving.

so

Ei = Ef
PEi = KEf + PEf

m g hi = ½m v² + m g hf

The new PE is m g hf = 10 * 9.8 * 2.5 = 245 J.
Since the object started with 10 * 9.8 * 5.0 = 490 J, the KE must be the difference... 490 - 245 = 245 J.

That makes since. Halfway down, the object has converted half of its PE to KE, so they should be equal.

To finish the problem...

245 = KE
245 = ½ m v²
245 = 0.5 * 10 * v²
v = 7 m/s

Answer 2

Delta PE = (5-2.5)mg = -2.5*10g Nm
Delta KE = -Delta PE = +2.5*10g Nm = 10*V²/2→V = √(5g)