Question

Assume that the equator of the Earth is 24,000 miles long (that’s its circumference). Now, pretend that you are standing somewhere on the equator, such as in the country of Ecuador. Now, if the Earth turns once, completely, in 24 hours, then, how fast would you be going (in miles per hour), even if you just stood still?

Answer 1

Answer:

1000 mph

Explanation:

P = Perimeter = 24000 mi

r = Radius of the equator

t = Time taken to complete one rotation = 24 h

Perimeter of a circle is given by

$P=2\pi r\\\Rightarrow r=\dfrac{P}{2\pi}\\\Rightarrow r=\dfrac{24000}{2\pi}\ mi$

Angular speed is given by

$\omega=\dfrac{2\pi}{t}\\\Rightarrow \omega=\dfrac{2\pi}{24}$

Velocity if given by

$v=r\omega\\\Rightarrow v=\dfrac{24000}{2\pi}\times \dfrac{2\pi}{24}\\\Rightarrow v=1000\ mph$

The person would be going at a speed of 1000 mph