In the initial position, before the fall starts, the velocity is zero, so all energy is potential energy.
Then, just before hitting the ground, all energy is kinetic energy, since the height is zero on the ground.
In the process of falling, the initial potential energy is being converted in kinetic energy, but the sum of energies (that is, the total mechanical energy) is the same along the process.
So, to calculate the height, we can equate the initial potential energy to the final kinetic energy:
[tex]\begin{gathered} PE=KE \\ m\cdot g\cdot h=\frac{mv^2}{2} \\ gh=\frac{v^2}{2} \\ 9.81\cdot h=\frac{10^2}{2} \\ 9.81h=50 \\ h=5.1\text{ meters} \end{gathered}[/tex]Therefore the initial height is 5.1 meters.
