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w1q - Douglass Houghton Workshop Section 1 Mon Worksheet...

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Douglass Houghton Workshop, Section 1, Mon 12/5/11 Worksheet Quandries 1. (Adapted from a Winter, 2005 Math 115 exam) Becky nor- mally plays the clarinet and flute, but one day Erin con- vinces her to climb to the top of Burton tower and com- mandeer the carillon, so that Erin can dance to the music. (Erin dances in many styles, but this is a new one, and it demands a dramatic debut.) Since Becky locked the door on her way up, Andrew, as part of his ROTC training, is given the mission of climbing up the side of the tower to retake the bells. Assume Erin is 30 ft from the base of the tower, and θ is the angle she has to look up to see Andrew. (a) Find a formula for the rate of change of Andrew’s dis- tance from the point O with respect to θ . (b) If the distance from point O to Becky is 200 ft. and Andrew is climbing at a constant 8 ft/sec, what is the rate of change of θ with respect to time when Andrew reaches Becky? Becky O Andrew Erin θ x y 1 - u 2 u x 1 y 2. We are still carrying a ladder of length 1 down
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