Math141Fall03_relatedrates

Math141Fall03_relatedrates - ADDITIONAL RELATED RATE...

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ADDITIONAL RELATED RATE PROBLEMS 1. A ladder 20 feet long leans against a vertical building. If the bottom of the ladder slides away from the building horizontally at a rate of 2 ft / sec, how fast is the ladder sliding down the building when the top of the ladder is 12 feet above the ground? Answer: Draw a picture of a wall of a building with a ladder leaning against it, letting x represent the distance from the base of the building to the bottom of the ladder, and with y denoting the distance from the ground to the top of the ladder. From the prob- lem’s statement, dx/dt = 2 feet per second. We wish to find dy/dt ’s value when y = 12. From the Pythagorean Theorem, x 2 + y 2 = 400, thus differentiating with respect to t we have 2 x dx dt + 2 y dy dt = 0, or, if y = 0, dy dt = - x y dx dt . Setting y = 12 and using the equation x 2 + y 2 = 400, we have x 2 = 256 or x = 16. Thus, dy/dt = - 8 / 3 ft / sec when y = 12. 2. At 1:00 P.M., ship A is 25 miles due south of ship B. If ship A is sailing west at a rate of 16 mi /
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