Related Rates Part II

 Group Exercises

  1. At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at the rate of 20 cubic feet per minute.  The diameter of the base of the cone is approximately three times the altitude.  At what rate is the height of the pile changing when it is 10 feet high?

  2. A boat is pulled by means of  a winch on the dock 12 feet above the deck of the boat.  The winch pulls in rope at the rate of  3 feet per second.  Determine the speed of the boat when there is 13 feet of rope out.  

  3. Two cars start moving from the same point.  One travels south at 60 m/hr and the other travels west at 25 m/hr.  At what rate is the distance between the cars increasing two hours later?

  4. A light shines from the ground onto a wall 25 feet away.  A man that is 6 feet tall walks away from the spotlight at a rate of 2 feet per second.  How fast is the height of his shadow decreasing when he is 10 feet away from the light?

  5. Boyle's Law states that when an ideal gas is compressed, the product of the volume and the pressure stays constant.  A cylindrical piston with radius 2 inches and height 12 inches is compressed at a rate of 3 cm3/sec.  If the pressure is 80 kPa when the cylinder is at fully extended, how fast is the pressure increasing when the cylinder is compressed to a height of 4 inches? 

  6. The minute hand of a clock is 8 inches long and the hour hand is 4 inches long.  How fast is the distance between their tips changing at 4 o'clock?

  7. You are watching a track meet where the runner is running along the circular track of radius 100 m at a rate of 7 m/sec.  Your seat is 200 m from the center of the track  How fast is the distance between you and the runner changing when the runner is 200 m from you?


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