A ball rolling down a hill is an example of a spontaneous process because it is driven by gravity without the need for an external energy source, making it a natural occurrence.
The question relates to the concept of spontaneous processes, which in the context of physics and chemistry, are processes that occur naturally under certain conditions without the need for a continual input of energy from an external source. Considering the options provided, a ball rolling down a hill would be an example of a spontaneous process. This is because the ball is moving in response to gravity, a natural force, which does not require an outside energy source to make it happen. On the other hand, a ball being rolled up a hill, a ball bouncing around from an initial input of energy, and a ball falling to Earth (indicating an input of energy by lifting the ball prior to it falling) exhibit characteristics of nonspontaneous processes as they rely on external forces or energy inputs to occur.