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Bernard is drunk and decides to a conduct an experiment. He decides to play with his tank of salt water. Water flows into a Bernard’s cylindrical tank at 15 cubic meters per minute. The tank initially contains $1000\pi$ cubic meters of water and has a height of 15 m. The tank holds 50 pounds of salt. Bernard makes sure that the tank is well-mixed. There is a hole in the cylinder that causes it to drain at a rate of 15 cubic meters per second. Bernard drops a pebble (at the tip of the cylinder with a velocity of 0) that will entirely cover the hole (not considering air or water resistance but only the force of gravity). (a) What is the rate of change of the amount of salt with respect to time at the moment Bernard drops the pebble? (b) What is the amount of salt left at the moment the leak is stopped?

**Posted:** Sat Oct 31, 2009 2:13 pm

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