Question

question 15 (problem reference 5 - 3) the earth rotates once per day about an axis passing through the north and south poles, an axis that is perpendicular to the plane of the equator. assuming that the earth is a sphere with a radius of 6.38 x 10^6 m, determine the speed of a person located at the equator. 464 m/s 11,100 m/s 1,770 m/s 73.8 m/s

Explanation:

Step1: Find the circumference of the Earth at the equator

The formula for the circumference of a circle is $C = 2\pi r$, where $r$ is the radius of the Earth. Given $r = 6.38\times10^{6}\text{ m}$, so $C=2\pi\times(6.38\times 10^{6}\text{ m})$.

Step2: Determine the time for one - rotation

The Earth rotates once in a day. One day has $t = 24\text{ h}\times3600\text{ s/h}=86400\text{ s}$.

Step3: Calculate the speed

Speed $v=\frac{d}{t}$, and here $d = C$. So $v=\frac{2\pi\times(6.38\times 10^{6}\text{ m})}{86400\text{ s}}\approx 464\text{ m/s}$.

Answer:

$464\text{ m/s}$