An object is let in free fall from a platform 20m high above Earth's surface. Describe the event in terms of energy and thus determine the speed of the object when it hits ground. Air resistance is negligible and gravitational acceleration is constant.
When the object is at rest on the platform it has no kinetic energy, but only potential energy. The potential energy is mgh where m is the mass of the object, g the gravitational acceleration and h the height of the object before falling. During free fall, the height of the object decreases and so does potential energy, and the speed increases, and with it kinetic energy increases. There is an exchange between potential and kinetic energy. When the object hits the ground there is no potential energy because the height is zero and its energy is only kinetic, 1/2mv2, where v is the speed of the object when it hits the ground. Using the law of energy conservation we deduce that the initial potential energy (mgh) was completely converted in kinetic energy at ground level (1/2mv2) and by equating these two we get v to be sqrt(2gh) so 19.8 m/s.
