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$$ \begin{array}{l}{\text { A heavy rainstorm dumps } 1.0 \mathrm{cm} \text { of rain on a city } 5 \mathrm{km} \text { wide }} \\ {\text { and } 8 \mathrm{km} \text { long in a } 2 \text { -h period. How many metric tons }} \\ {\left(1 \text { metric ton }=10^{3} \mathrm{kg}\right) \text { of water fell on the city? }\left(1 \mathrm{cm}^{3} \text { of }\right.} \\ {\text { water has a mass of } 1 \mathrm{g}=10^{-3} \mathrm{kg} . \text { ) How many gallons }} \\ {\text { of water was this? }}\end{array} $$

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Physics 101 Mechanics

Chapter 1

Introduction, Measurement, Estimating

Physics Basics

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Winnipeg

McMaster University

Lectures

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

09:56

In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

05:10

A heavy rainstorm dumps 1.…

02:55

A storm dumps 1.0 cm of ra…

02:11

02:50

What mass of water fell on…

02:35

07:21

Solve the given problems.D…

03:37

(II) Rain is falling at th…

04:21

Meteorology If 3 in. of ra…

04:22

01:26

One cubic centimeter of wa…

So how many metric tons of water fell on the city and how many gallons of water fell in the city? So we can say that the area of the city of 40 square kilometers and we have a depth of one centimeter so we can say 40 square kilometers multiplied by 10 to the fifth centimeters. For every one kilometer we can square this entire term. We're gonna multiply this by one centimeter because I would be the depth um multiplied by 10 to the negative third kilograms for every one centimeter. Cute. This would be the density of water. And then we have for every one metric ton there there are 1000 kilograms, so 10 to the third kilograms. And so we have four times 10 to the fifth metric tons of water. After that, we can do the exact same thing. However, will say 40 kilometers squared will have the same conversion 10 to the fifth centimeters for every one kilometer square this entire term, we're gonna multiply it by again. One centimeter. Uh, we can say that for every one leader of water, there are 10 to the third cubic centimeters. So this would be again the density of water in terms of leaders per centimeters of person per cubic centimeters. And then for every one gallon there are 3.78 leaders. So I'd be the volume of one gallon of water or what? Just simply one gallon. And so in gallons, we have 1.6 times 10 to the eighth gallons of water on the city. That is the end of the solution. Thank you for watching.

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