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If you began walking along one of Earth's lines of longitude and walked north until you had changed latitude by 1 minute of arc (there are 60 minutes per degrce), how far would you have walked (in milcs)? This distance is called a "nautical mile."

1.15 $\mathrm{mi}$

Physics 101 Mechanics

Chapter 1

Introduction, Measurement, Estimating

Physics Basics

Cornell University

Hope College

University of Sheffield

McMaster University

Lectures

04:16

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Gar question says that if you begin walking along one of Earth's lines of longitude and walked to north until you had changed latitude by one minute of arc, there are 60 minutes per degree. How far would you have walked in miles? This is a distance call nautical miles. So we're going to utilize the fact that walking completely around the earth along the meridian would trace out a full circle whose three, which is 360 degrees and that would be equal to the circumference of the earth. Okay. Ah, so I went ahead here and wrote down what was given, which is the distance is one minute. That's what we're walking and one degree is equal to 60 minutes on. Then I also wrote down the radius of the Earth, which is 6.38 times tender, that they're kilometers, because we're going to need to use that. And the question is, what's the distance in miles, right? We want to find the distance in miles and we know it in minutes. So and also, as I previously mentioned, we're going to utilize the fact that 360 degrees is one complete walk around the earth, which is this equal. So seat 360 degrees is equal to the circumference of the earth, which is equal to two pi times the radius of the earth. Okay, All right. So now let's go ahead and start working our conversion. So we're going to start out with what we know, which is The distance is equal to one minute. Okay? And we're going to multiply that by our conversion from minutes two degrees. Okay, so one degree is equal to 60 minutes of arc. Okay, now that we have in minutes of arc we wanted I'm sorry that we have it in degrees. We want to convert that to greet degrees into meters. And we know the conversion from degrees and the meters. It's ah, we're going. And we know that based upon the circumference of the earth, because to pie, at times the radius of the earth which is 6.38 times 10 to the third kilometers. Write that out is our circumference to Clyde times 6.3 attempts sent their kilometers, and that is the equivalent to 360 degrees around the earth. Okay, so now if we carry out this operation. We have it from units of minutes now into units of kilometers. But we're asked for units of miles. So the last thing we're going to do is convert this team. It's of miles by using the fact that 0.6 to 1 miles is in every kilometer. Okay. And if you carry this out and type all this in your calculator, you will have 1.15 miles as your distance. Box it in. There's your solution.

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