“How does a baseball outfielder know where to run to catch a fly ball? The “outfielder problem” remains unresolved, and its solution would provide a window into the visual control of action. It may seem obvious that human action is based on an internal model of the physical world, such that the fielder predicts the landing point based on a mental model of the ball's trajectory.” Journal of Vision, 2009 Dec 14;9(13):14.1-8.
The problem is a part of the much wider puzzle of how animals are able to 'plot' trajectories, apparently effortlessly - for example in hunting animals which intercept the 'future' path of their prey. It has been studied in wide variety of animals from flies, fishes, birds, and mammals.
There is no agreed explanation as to how these animals are able to quickly compute trajectory paths in three dimensions. Even more complexity is apparent in paths which involve gravity (or any other acceleration or deceleration), in this case, from a mathematical standpoint at least, some form of calculus is required to correctly predict paths. The underlying neural mechanisms of these computations is entirely unknown.