Yachts that compete in the America\'s Cup must satisfy the International America

Question

Yachts that compete in the America's Cup must satisfy the International America's Cup Class rule that requires L + 1.25 squareroot s - 9.8^3 squareroot D = 16.296 meters. where L represents the yacht's length in meters, S represents the rated sail area, in square meters, and D represents the water displacement, in cubic meters. Is a yacht having length 21.85 meters, sail area 305.5 square meters, and displacement 21.85 cubic meters eligible to compete? Explain. Explain why the units of your numerical answer in part a are meters.

Explanation / Answer

a. If the length of the yatch is L = 21.85 meters, sail area is S = 305.5 sq. meters and the displacement is D = 21.85 cu.meters, then L+1.25S -9.8(D)1/3 = 21.85 + 1.25(305.5)1/2 -9.8(21.85)1/3 = 21.85+ 1.25(17.4786)- 9.8(2.7957) = 21.85+ 21.84825 - 27.39786 = 16. 30039 , say 16.3000 meters 16.296. Hence The given yatch is not eligible to compete.

b. The square root of a number in square meters is a number in meters and the cube root of a number in cubic meters is a number in meters. Hence the units of the numerical answer is in meters.

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