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Sagot :
[tex]v=wr[/tex][tex]w=\frac{2\pi}{T}[/tex]
The equations are the linear velocity and angular moment respectively.
Since we have that the rotation of the Earth takes 24 hours, we transform it into seconds, that is:
[tex]24\cdot60\cdot60=86400[/tex]So, it has a period of 86400 seconds.
We now, transform the radius to the IS (from miles to meters), that is:
[tex]3961.3\text{miles}=6375.1\operatorname{km}[/tex]And, since the latitude is 68.4711° we solve in the function given at the start, that is:
[tex]w=\frac{2\pi}{86400}\Rightarrow w=7.272205217\cdot10^5[/tex]Then we divide this value by the time it takes to do a revolution of the Earth, the previously calculated 86400 seconds, that is:
[tex]v=wr\Rightarrow w=(7.272205217\cdot10^{-5})(6375.1)[/tex][tex]\Rightarrow v\approx0.464[/tex]So, the linear velocity at that latitude is approximately 0.464 Km/s.
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