Displacement Question: Flat Earth vs. Spherical Earth

In summary, the person will be 5km southeast from the camp if the Earth is assumed to be flat. However, if the Earth is not assumed to be flat and is instead spherical, the person will end up back at the North Pole if they walk 8km south, 3km east, and then 4km north. This is because traveling north 8km on a spherical Earth will bring the person back to their starting point at the North Pole.
  • #1
Emethyst
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0

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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  • #2
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?
 
  • #3



I must approach this question with an open mind and gather all available information before making any assumptions or conclusions. In this case, the key information that is missing is the size and shape of the Earth. Without this information, we cannot accurately determine the displacement of the person from the camp.

If we assume that the Earth is spherical, we can use the Pythagorean theorem to calculate the displacement. However, the result will be different depending on the size of the Earth. For example, if we assume the Earth has a radius of 6,371km (the average radius of the Earth), the person's displacement would be approximately 5.5km SE. However, if we assume the Earth has a larger radius, the displacement would be even greater.

On the other hand, if we assume that the Earth is flat, the displacement would be the same as in part a) - 5km SE. However, this assumption is not supported by scientific evidence and is not a valid representation of our planet.

Therefore, in order to accurately determine the displacement, we need to know the size and shape of the Earth. Without this information, it is impossible to provide a precise answer for part b). I would suggest further research and investigation to gather the necessary information before making any conclusions.
 

FAQ: Displacement Question: Flat Earth vs. Spherical Earth

What is simple displacement?

Simple displacement is a basic concept in physics that refers to the change in position of an object in a given direction. It is usually measured in meters (m) or centimeters (cm) and can be represented by the symbol "d".

How is simple displacement different from distance?

Simple displacement is a vector quantity that takes into account the direction of the change in position, while distance is a scalar quantity that only considers the magnitude of the change in position. This means that simple displacement tells us not only how far an object has moved, but also in which direction it has moved.

What is the formula for calculating simple displacement?

The formula for calculating simple displacement is: d = xf - xi, where "d" is the displacement, "xf" is the final position, and "xi" is the initial position. For example, if an object starts at position 5 meters and ends at position 10 meters, the displacement would be 10m - 5m = 5m.

Can simple displacement be negative?

Yes, simple displacement can be negative. This occurs when an object moves in the opposite direction of the reference point or starting point. For example, if an object starts at position 10 meters and ends at position 5 meters, the displacement would be 5m - 10m = -5m.

How is simple displacement related to velocity?

Simple displacement and velocity are closely related. Velocity is the rate of change of an object's displacement over time, and it is calculated by dividing the displacement by the time it took to make that change. In other words, velocity = displacement / time. This means that the greater the displacement of an object over a certain amount of time, the greater its velocity will be.

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