Houdini’s Great Escape Jordan Burnett Calculus II Honors Dr. Cruz-White

Harry Houdini Born on April 6, 1874 in Appleton, Wisconsin. Began his magic career at the age of 17 in front of civic groups. Performed multiple tricks including “Metamorphosis” in which he and an assistant would switch places after he was placed inside a crate. Was mostly recognized for his amazing ability to escape from numerous restraints and apparatuses. Often said that he was able to withstand any blow to the stomach. Ironically, this led to his untimely death after he developed peritonitis from three shots to the gut which caused his appendix to burst.

Something that you didn’t know about Houdini: One of the Magician’s secrets is that he used Calculus to perform his tricks.

The Great Escape Houdini performed a trick in which he was locked in chains and shackled down to a stool attached to the bottom of a giant tank. The tank was then filled with water. Houdini would have to escape the restraints before the water rose above his head and cause him to drown.

The Great Escape Houdini knew that it would take him exactly ten minutes to escape the chains. Being a showman, he wanted to wait until the last second, when the water level had just risen over the top of his head, to set himself free. Standing at six feet tall and knowing the rate at which the water filled up the tank, Houdini used calculus to find out at what height the stool needed to stand.

Above is a diagram of the tank that the stunt was performed in showing the diameter at one foot intervals.

What you need to know: 1 ≤ y ≤ 13 1 gallon = 0.13368 cubic feet Formula for Volume about the y-axis: You must neglect the volume of the Magician himself as well as the volume of the stool on which he stood. 1 gallon = 0.13368 cubic feet The tank is filling up at 500 gallons per minute. The tank is a shape formed by a function revolving about the y axis. R(y) = 10/(y)1/2

Applying Calculus 0.13368 cubic ft x 500 gallons x 10 minutes = 668.4 cubic ft = V 1 gallon minute V = пʃ1h 100/y dy => 100п ʃ1h 1/y dy => 100п ln(y) 688.4 cubic ft. = 100п ln(h) 2.13 = ln(h) => h = 8.39 = Height of water Height of Water – Height of Houdini 8.39 ft – 6 ft = 2.39ft

Houdini’s stool would have to stand 2.39 inches tall!

References Appleton History www.apl.org/histoy/houdini/biography.html Wheaton College <http://wheatoncollege.edu/Academic/academicdept/MathCS/Faculty/tratliff/writing/calculus-II/escape.html>