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Houdini's esape Calculus problem! Part 1.?
Houdini had his feet shackled on top of a block which was placed on the bottom of a giant laboratory flask. The cross sectional radius of the flask, measured in feet, was given as a function of height "z" from the ground formula
r(z)= 10/(squareroot "z"), with the bottom of flask @ z=1ft. Flask was filled w/ water at rate of 22pi cubic ft/min. Houdini had 10 mins to escape, he wanted it precisely when the Water Level reach top of his head. Houdini is 6ft tall.
A) Find out how high this block is. Express volume of water in flask as funct of height of the liquid Above Ground level. What is the vol when water level reach top of his head? (Neglect his vol and vol of block) What is height of block?
B) h(t)=height of water above grnd level @ time "t". Houdini dervives the equ for rate of change dh/dt as funct of h(t) itself. Dervive the equ. How fast is water level changing when flask starts to fill. How fast is changin when water reach his head? Express h(t) as a function of time.
See here:
http://www.mathgoodies.com/forums/topic.asp?TOPIC_ID=33386
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