The design of boats is based on Archimedes' Principle, which states
that the buoyant force on an object in water is equal to the weight of
the water displaced. Suppose you want to build a sailboat whose hull
is parabolic with cross section , where is a constant.
Your boat will have length and its maximum draft (the maximum
vertical depth of any point of the boat beneath the water line) will
be . See the figure below.
(Click on the figure for a larger version.)
Every cubic meter of water weighs newtons. What is the
maximum possible weight for your boat and cargo?
weight = newtons