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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?

  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?

  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?

  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.

  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?

  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.