19-related-rates

19-related-rates - Math 1a 1 Related Rates Fall 2009 Two...

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Math 1a Related Rates Fall, 2009 1 Two cars are approaching an intersection. A red car, approaching from the north, is traveling 30 feet per second and is currently 60 feet from the intersection. A blue car, approaching from the east, is traveling 20 feet per second and is currently 80 feet from the intersection. How fast is the distance between the two cars decreasing? 2 A winch is pulling a boat toward a dock. The winch pulls the line in at a constant rate of 2 feet per second. The rope leaves the winch 14 feet above (vertically) where it connects to the boat. How fast is the boat moving (horizontally through the water) when it is 48 feet from the dock? 3 A plane going 300 mph passes immediately overhead an observer on the ground, at a height of 5 miles. How fast is the distance between the observer and the plane changing 5 minutes later? (Assume the plane’s speed is constant.)
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4 A weather balloon is being filled with helium from a tank at a constant rate of 20 cubic feet per second. Assume that at any particular moment the balloon is a sphere.
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