How to Use Archimedes' Principle to Find the Maximum Weight a Boat Can Hold

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 y=ax^2, where a is a constant. Your boat will have length L and its maximum draft will be H. Every cubic meter of water weighs 10,000 newtons. What is the maximum possible weight for your boat and cargo? First find the volume using cross-sectional areas and integral calculus. The answer depends on a, H, and L. Infinite Powers: https://amzn.to/3ucUVu3 (How Calculus Reveals the Secrets of the Universe).

#calculus #archimedesprinciple #volume

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