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(III) You are in a hot air balloon, 200 $\mathrm{m}$ above the flat Texas plains. You look out toward the horizon. How far out can you sec-that is, how far is your horizon? The Earth's radius is about 6400 $\mathrm{km}$ .

$5 \times 10^{4} m$

Physics 101 Mechanics

Chapter 1

Introduction, Measurement, Estimating

Physics Basics

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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.

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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.

03:26

(III) You are in a hot air…

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04:50

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You are in a hot air ballo…

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You are flying in a jetlin…

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An airplane reaches an alt…

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At an altitude of $m$ mile…

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How Far Can You See? Becau…

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So we simply want to find out how how far horizon is. We can drop the diagram. Um, going here, meeting here. Okay, so this would be a tch. This would be D. This would be our and this would be our here we can use our would simply be equal to the radius of the earth So we can say that our plus h squared equals R squared plus d squared according to Pythagorean theorem. Could be this would become R squared plus two R h plus h squared with equal r squared plus d squared. We can see that the R is gonna cancel out the are square terms or canceling out. So we have to our age plus h squared, equaling d squared And then we can solve for D So D is gonna equal to our age Plus h squared all to the 1/2 power and we can solve so d going equal to times 6.4 times 10 to the sixth meters that diameter rather the radius of the earth. My apologies, multiplied by 200 meters are height plus again, 200 meters squared and all to the 1/2 power We find that the distance of our horizon is going to be 5.1 times 10 to the fourth meters. And if you use the conversion, it's going to be approximately 80 miles. That is the end of the solution. Thank you for watching.

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