Energy changes in a falling ball

A $1.2\ \text{kg}$ ball is dropped from $25\ \text{m}$. You will make the program follow its potential, kinetic and total energy as it falls, and find when the first two are equal.

The idea. After a time $t$ the ball has fallen $\tfrac12 gt^2$ and moves at $gt$. So $U = mgh$ falls as $K = \tfrac12 mv^2$ grows, and their sum stays the same.

Your tasks.

1. Work out the height at every time in t.
2. Work out the potential energy U and the kinetic energy K at every time.
3. Find the time at which U and K are closest to equal.