Displacement Question: Flat Earth vs. Spherical Earth

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SUMMARY

The discussion centers on a displacement problem involving a person walking from the North Pole under two assumptions: a flat Earth and a spherical Earth. The solution for the flat Earth scenario, calculated using Pythagorean's theorem, results in a distance of 5 km southeast from the starting point. For the spherical Earth scenario, the person walks south 8 km, east 3 km, and then north 4 km, ultimately ending up 4 km from the North Pole, demonstrating the unique properties of spherical geometry. The problem illustrates the differences in displacement calculations based on the Earth's shape.

PREREQUISITES
  • Understanding of Pythagorean's theorem
  • Basic knowledge of spherical geometry
  • Familiarity with coordinate systems
  • Concept of geodesics on a sphere
NEXT STEPS
  • Study spherical geometry and its applications in navigation
  • Explore the concept of geodesics and their significance in real-world scenarios
  • Learn about coordinate transformations between flat and spherical models
  • Investigate practical examples of displacement calculations on a spherical Earth
USEFUL FOR

This discussion is beneficial for students in geometry, physics enthusiasts, and anyone interested in understanding the implications of Earth's shape on navigation and displacement calculations.

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Homework Statement


Suppose a person has set up camp at the North Pole. If the person walks 8km south, then 3km east and finally 4km north, how far from the camp will the person be if a) it is assumed the Earth is flat? b) it is not assumed the Earth is flat.



Homework Equations


Pythagorean's theorem.



The Attempt at a Solution


I have solved for a) no problem (answer is 5km SE), the only part I'm having trouble with is b). Because no information is given concering a spherical Earth in the question, I'm guessing that it just might be a trick question, but I'm not sure. If someone can help me with part b) for this question it would be great, thanks in advance.
 
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For a spherical Earth, if we go south 8km, go east 3km, then go north 8km then we end up back at the north pole. Can you see/understand why? So using the same idea, what if we only go north 4km?
 

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