A 100 kg person falls off of a 20 m cliff. Assume the acceleration due to gravity is g = 9.8 N/kg. How much kinetic energy does the person gain...

Hello!

It is simple: the total energy is conserved, i.e. the total energy at the start and at the finish are the same. In this problem, energy exists in potential and kinetic states. 

At the start kinetic energy is zero and potential energy measured off the ground level is  `mgh` (a known formula). So the total energy is  `mgh.`

At the finish the potential energy is in turn zero, so the total energy is only kinetic.

So the kinetic energy gained is  `mgh=100*9.8*20` =19600 (J). This is the answer.

There is another method: we can find the speed `V` from the formulas of free-fall motion and compute the kinetic energy by the known formula  `(m V^2)/2.` The result will be the same.

Of course we ignore air resistance here, which is far from reality.