Question

The lattitude of lubbock texas (known as the hub city of the south plains)is 33N. What is its rotational speed, assuming that the radius of earth at the equator to be 63km?

Answer 1

In the task, obviously a typo. Equatorial Earth Radius - 6371km

$$R_{33°}=Rcos\alpha$$

rotational speed at latitude 33°:

$$V_{33°}=\frac{2\pi\cdot{R_{33°}}}{T}=\frac{2\pi\cdot{Rcos\alpha}}{T}$$

the period of rotation of the earth around its axis

$$T=24h$$

$$V_{33°}= 1398km/h$$

Answer: 1398km/h or 388m/s