w2p - Douglass Houghton Workshop, Section 2, Thu 12/1/11...

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Douglass Houghton Workshop, Section 2, Thu 12/1/11 Worksheet Partridge 1. (This problem appeared on a Winter, 2008 Math 115 exam) A bellows has a triangluar frame made of three rigid pieces. Two pieces, each 10 inches long, are hinged at the nozzle. They are attached to the third piece at points A and B which can slide, as shown in the diagrams below. (The Fgures show a 3D sketch of the bellows and a 2D sketch that may be speciFcally useful to solve the problem.) Each piece of the frame is 2 inches wide, so the volume (in cubic inches) of air inside the bellows is equal to the area (in square inches) of the triangluar cross-section above, times 2. Suppose you pump the bellows by moving A downward toward the center at a constant speed of 3 in/sec. (So B moves upwards at the same speed.) What is the rate at which air is being pumped out when A and B are 12 inches apart? (So A is 6 inches from the center of the vertical piece of the frame.) b b b nozzle A B h 10 10 b 2. (This problem, like all Awkward Turtle problems, appeared on a Winter 2009 Math 115
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w2p - Douglass Houghton Workshop, Section 2, Thu 12/1/11...

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