Use this method to find how the speed with which animals of similar shape can run up a hill depends on the size of the animal. Let L represent some characteristic length, such as the height or diameter of the animal. Assume that the maximum rate at which the animal can do work is proportional to the animal's surface area: Pmax ∞ L2. Set the maximum power output equal to the rate of increase of gravitational potential energy and determine how the speed v depends on L?