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.
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Calculus II Honors
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.
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.
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