The Boat Challenge

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The Boat Challenge
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Materials

• One 8.5 x 11 inch sheet of laminated paper
• Scotch tape
• Scissors
• Ruler

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Design/Build Boats

• Build a rectangular boat that will hold the most
  weight without sinking.

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Requirements

• Boat must have a name.
• Boat must have a flag.
• Boat must be completed in 20 minutes.

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Test Boats

• Place boats in the tub of water.
• Apply weights until the boat sinks.
• Count the total mass the boat was able to carry
  (not including the mass that caused the boat to
  sink)
• Note Most boats carry several hundred grams.
  Be sure to use heavy mass first.

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Volume is the quantity of interest

• Buoyancy A boat floats when its weight is
  displaced in water.
• Therefore the best boat will displace the most
  water.

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Design the boat with Maximum Volume

• Write a function for volume.
• Maximize the function.

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Functions for Volume

• f(h) (11 2h)(8.5 2h)(h)
• f(h) 4h3 39h2 93.5h

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Maximize using Calculus

• 1st Derivative f(h) 12h2 78h 93.5
• Set f(h) 0 and solve for h
• 12h2 78h 93.5 0
• h 78 (782 (4)(12)(93.5))0.5
• (2)(12)
• h 4.915 inches 1.585 inches

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Which is my solution?h 4.915 or 1.585 inches

• 2nd Derivative f(h) 24h 78
• f(4.915) 39.96 and f(1.585) -39.96
• f(1.585) 66.158 inches cubed

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Optimization

• One of the most powerful tools math-ematics
  offers industry is optimi-zation. The ability to
  predict and design the best specimen given
  various goals and constraints is lucrative.

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New Challenge

• Given an 8.5 x 11 inch sheet of paper, build the
  best canoe.
• Canoe triangular ends and one crease down the
  middle.

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New Challenge
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• Canoe triangular ends folded up at 90 and
  one crease down the middle.