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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69

Problem 12 Medium Difficulty

You are driving into St. Louis, Missouri, and in the distance you see the famous Gateway-to-the-West arch. This monument rises to a height of 192 $\mathrm{m}$ . You estimate your line of sight with the top of the arch to be $2.0^{\circ}$ above the horizontal. Approximately how far (in kilometers) are you
from the base of the arch?

Answer

5.5 $\mathrm{km}$

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Physics 101 Mechanics

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Chapter 1

Introduction and Mathematical Concepts

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Video Transcript

All right, You're on car trips. Museum monument That right? It's 122 meters off the ground. You are very far away from it. So it appears. All right, here's your landing site. Hears you. It appears two to be about two degrees above the horizontal. All right, so we're gonna use some, uh, tricky to find the distance X right here. That this since you are from this monument. So we have the adjacent side of this triangle and we have the opposite side. We're missing the high partner, so we won't use Ah. Where's the apartment? Straight. Here's the occasion. Side here's the opposite side. During used the opposite in the adjacent sides to solve this equation. So if we use a tangent, engines off two degrees is equal opposite over adjacent. No, wait. I need you. Here is so for X so we can multiply both sides by x two x 10 Move. Two degrees is equally at 192 meters and divide both sides by tangent of two degrees and you get X is equal to 192 meters over tangent of two degrees. And if you put that into your calculator, you'll get that X is you could do 5000 498 meters. And if we convert that two kilometers, you will get that it is abolished 5.5 kilometers because there are 1000 kilometers. And when Oh, excuse me. 1000 meters and one kilometers, we divide. Um, this number right here by 1000. So we get the decimal place moves over three spots. So 12 and three right there. So 5.5 kilometers.

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