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The flask will be filled with water (at a constant rate of 500 gallons per minute). It will take me exactly 10 minutes to escape from the chains. The diameter of the tank at 1 foot intervals. 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. A gallon is equal to 0.13368 cubic feet.  You can think of the volume and the height of the water as functions of time. You can easily find an expression for V (t), and then use your expression for volume in terms of height to solve for h(t).

The flask will be filled with water (at a constant rate of 500 gallons per minute). It will take me exactly 10 minutes to escape from the chains. The diameter of the tank at 1 foot intervals. 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. A gallon is equal to 0.13368 cubic feet.  You can think of the volume and the height of the water as functions of time. You can easily find an expression for V (t), and then use your expression for volume in terms of height to solve for h(t).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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  • The flask will be filled with water (at a constant rate of 500 gallons per minute).
  • It will take me exactly 10 minutes to escape from the chains.
  • The diameter of the tank at 1 foot intervals.
  • 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.
  • A gallon is equal to 0.13368 cubic feet. 
  • You can think of the volume and the height of the water as functions of time. You can easily find an expression for V (t), and then use your expression for volume in terms of height to solve for h(t).
5.5 t 5.7 A 6f 6.3 A 6.7t 7t 7.5A 8.1 A 8.9 fA 10ft 11.5 t 14ft 20ft 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. Yours sincerely, T. Houdini A Few Comments After consulting with T. Houdini, I have a few suggestions that may help you get started: •A gallon is equal to 0.13368 cubic feet. • You can think of the volume and the height of the water as functions of time. You can easily find an expression for V (t), and then use your expression for volume in terms of height to solve for h(t).
Transcribed Image Text:5.5 t 5.7 A 6f 6.3 A 6.7t 7t 7.5A 8.1 A 8.9 fA 10ft 11.5 t 14ft 20ft 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. Yours sincerely, T. Houdini A Few Comments After consulting with T. Houdini, I have a few suggestions that may help you get started: •A gallon is equal to 0.13368 cubic feet. • You can think of the volume and the height of the water as functions of time. You can easily find an expression for V (t), and then use your expression for volume in terms of height to solve for h(t).
Questions: 1. 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? 2. So at any time after the water begins flowing, I want to know how high the water is in the tank? how fast the water is rising? 3. I would like to know how long I will have to hold my breath during the last part of the stunt.
Transcribed Image Text:Questions: 1. 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? 2. So at any time after the water begins flowing, I want to know how high the water is in the tank? how fast the water is rising? 3. I would like to know how long I will have to hold my breath during the last part of the stunt.
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