The Great Escape

T. Houdini
135 Prestidigitator Avenue
Handcuff, WI 59055
October 15, 1997

Math 104 Students
Wheaton College
Norton, MA 02766
Dear Calculus Students:

I have decided to continue the family business established by my grandfather, and I need some help planning one of the escapes that I am including in my inaugural tour. When I went looking for help, your enterprising and resourceful professor naturally referred me to you.

I will be locked in chains and have my feet shackled to the top of a stool which is attached to the bottom of a giant tank that looks vaguely like a laboratory flask. The flask will be filled with water (at a constant rate of 500 gallons per minute), and after much practice out of the water, I have determined that it will take me exactly 10 minutes to escape from the chains.

I have a flair for the dramatic, so I would like to escape from the shackles at the exact instant that the water reaches the top of my head. I need your help in determining how tall the stool should be. Also, I want to monitor the rise of the water during the escape, so at any time after the water begins flowing, I want to know how high the water is in the tank and how fast the water is rising. While I am fairly accomplished at holding my breath under water, I would like to know how long I will have to hold my breath during the last part of the stunt.

I've included a sketch of the tank below, which gives the diameter of the tank at 1 foot intervals.

After consulting with your enterprising and resourceful professor, he suggested that you might be interested to know that I am 5 feet 9 inches tall, and I'm pretty skinny so that you can ignore both my volume and the volume of the stool in your analysis.

I realize that this is a busy time of year for you, but I would greatly appreciate an answer by October 24, since my tour opens at the Howard Johnson's in Kenosha on Halloween weekend.

Yours sincerely,
T. Houdini

After consulting with T. Houdini, I have a few suggestions that may help you get started: