Calgary,Canada is at a latitude of 51.0 degrees north.How fast is Calgary moving eastward as the Earth rotates? (The radius of the earth is 6370 km)
A)0 km/h
B)1050 km/h
C)1300 km/h
D)1520 km/h
E)1670 km/h

Question

Quizplus · Accepted Answer

The speed at which a point on the Earth's surface moves due to the Earth's rotation can be calculated using the formula $v = \omega r$, where $v$ is the linear velocity, $\omega$ is the angular velocity of the Earth (in radians per hour), and $r$ is the radius of the circular path that the point takes due to the Earth's rotation. The angular velocity of the Earth is approximately $2\pi$ radians per 24 hours, or $\frac{2\pi}{24}$ radians per hour. However, because Calgary is at a latitude of 51 degrees north, we must adjust the radius to account for the Earth's curvature at that latitude, which is $r = R \cos(\text{latitude})$, where $R$ is the Earth's radius (6370 km) and the latitude is 51 degrees. Thus, the effective radius for Calgary's rotation around the Earth's axis is $6370 \times \cos(51^\circ)$. Plugging these values into the formula gives a speed less than the equatorial speed (approximately 1670 km/h) but significantly more than 0 km/h, leading to the correct answer after calculation being approximately 1050 km/h.

Calgary,Canada Is at a Latitude of 51