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).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hits:
- 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).

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).

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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