40. The earth has a radius of 6.38 x 10⁶ m and turns on its axis once every 23.9 h. (a) What is the tangential speed (in m/s) of a person living in Ecuador, a country that lies on the equator? (b) At what latitude (i.e., the angle q in the drawing) is the tangential speed one-third that of a person living in Ecuador?

At Equator R = R_E

At a latitude other than the equator the radius of rotation is not the Radius of the Earth, but it is a component as shown below. At an angle q, R -> R cos(q)

Now we want to know what latitude will this tangential speed will equal 1/3 the tangential speed at the equator.

ω is the same at the equator and at the latitude q, so we can cancel terms on both sides and we have

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