### Related Rates Greatest Hits

#### by Professor DeTurck

1. A light is at the top of a 16-ft pole. A boy 5 ft tall walks away from the pole at a rate of 4 ft/sec. At what rate is the tip of his shadow moving when he is 18 ft from the pole? At what rate is the length of his shadow increasing?
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3. A man on a dock is pulling in a boat by means of a rope attached to the bow of the boat 1 ft above the water level and passing through a simple pulley located on the dock 8 ft above water level. If he pulls in the rope at a rate of 2 ft/sec, how fast is the boat approaching the dock when the bow of the boat is 25 ft from a point on the water directly below the pulley?
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5. A weather balloon is rising vertically at a rate of 2 ft/sec. An observer is situatied 100 yds from a point on the ground directly below the balloon. At what rate is the distance between the balloon and the observer changing when the altitude of the balloon is 500 ft?
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7. The ends of a water trough 8 ft long are equilateral triangles whose sides are 2 ft long. If water is being pumped into the trough at a rate of 5 cu ft/min, find the rate at which the water level is rising when the depth is 8 in.
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9. Gas is escaping from a spherical balloon at a rate of 10 cu ft/hr. At what rate is the radius chaing when the volume is 400 cu ft?
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11. An airplane, flying at a constant speed of 360 mph and climbing at an angle of 45 degrees, passes over a point P on the ground at an altitude of 10,560 ft. Find the rate at which its distance from P is changing one minute later.