A point on Earth's surface in the northern hemisphere is moving eastward at 1300 km/h.What is the latitude of this point? (The radius of the earth is 6370 km) A)45^o north B)39^o north C)30^o north D)51^o north E)43^o north

Question

Quizplus · Accepted Answer

The point's speed can be related to the Earth's rotation speed at the equator (1670 km/h) and its latitude. The formula to find the latitude ($\lambda$) given the speed (v) at that latitude is $v = v_{equator} \cdot \cos(\lambda)$, where $v_{equator}$ is the speed at the equator. Rearranging for $\lambda$, we get $\lambda = \cos^{-1}\left(\frac{v}{v_{equator}}\right)$. Plugging in $v = 1300$ km/h and $v_{equator} = 1670$ km/h, we find $\lambda = \cos^{-1}\left(\frac{1300}{1670}\right)$, which gives a latitude close to 39 degrees north.

A Point on Earth's Surface in the Northern Hemisphere Is