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$$ \begin{array}{l}{\text { An average family of four uses roughly } 1200 \mathrm{L} \text { (about) }} \\ {300 \text { gallons) of water per day }\left(1 \mathrm{L}=1000 \mathrm{cm}^{3}\right) . \text { How much }} \\ {\text { depth would a lake lose per year if it uniformly covered an }} \\ {\text { arca of } 50 \mathrm{km}^{2} \text { and supplicd a local town with a population }} \\ {\text { of } 40,000 \text { people? Consider only population uses, and }} \\ {\text { neglect evaporation and so on. }}\end{array} $$

9 $\mathrm{cm} / \mathrm{year}$

Physics 101 Mechanics

Chapter 1

Introduction, Measurement, Estimating

Physics Basics

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

McMaster University

Lectures

04:16

In mathematics, a proof is…

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$$\begin{array}{l}{\te…

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$100(1.04)^{2 t}=300$

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so we want to do we want to find the death loss for the lake per year so we can say that the volume of water used by the people per year we can say that's around the lake. There are four times 10 to the fourth people that are drawing water from this lake and then at a rate of 1200 leaders per day for a single family. So we can say for people and then we're going to multiply it by 365 days in one year and then we can multiply that by 1000 cubic centimeters per one leader and then we want to playing that by one kilometer for every 10 to the fifth centimeters Quantity cube. And so we find that the use the usage would be 4.38 times 10 to the negative third cubic kilometers per year. And so at this point, we can say that the depth of the water is going to be equal to the volume of the water divided by the area, the surface air, the surface area of the lake, and this is gonna be equal to 4.38 times 10 to the negative third kilometers cubic kilometers per year. So that would be the volume that is being used divided by the surface area of the lake that is exposed thio essentially this week. If we wanted to model the lake as a cylinder Uh, the cross sectional area of the lake. Yeah, Kilometers squared. And so we can say that this is gonna be equal to 8.76 times 10 to the negative fifth, uh, kilometers per year and we should convert so we can say 10 to the fifth centimeters for every one kilometer. So the death would be essentially decreasing at a rate of 8.76 centimeters per year. That is our final answer. That is the end of the solution. Thank you for watching.

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