A person travels from A to B on land and the distance traveled is 2100 km. If the radius of the Earth is 6300 km, what is the person's displacement.

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justaguide eNotes educator| Certified Educator

A person goes from point A to point B. The distance traveled on land for this is equal to 2100 km. The magnitude of the person's displacement here is the length of a straight line drawn from A to B.

Assume the shape of the Earth to be a perfect sphere. The radius is 6300 km. If a cross-sectional circle is cut along the path traveled by the person, the angle between the line joining the center to point A and the radial line from point B is given by X where `X/360 = 2100/(2*pi*6300)`

=> `X = (360*2100)/(2*pi*6300) `

=> `X ~~ 19.09` degrees

The line joining point A and B and the radial lines from A and B form an isosceles triangle with equal sides of 6300 km and the the angle between them equal to 19.09 degrees. If a perpendicular is drawn from the center to the third side, it bisects the third side.

A right triangle is formed with `(D/2)/6300 = sin (19.09/2)` , where D is the displacement that has to be determined.

`D ~~ 2*6300*sin(19.09/2)`

=> `D ~~ 2090.29` km

The magnitude of displacement of the person traveling from A to B is approximately 2090.29 km

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