Question

The Earth rotates every 24 hr and as diameter of 7, 926 mi. If you're standing on the equator, how fast are you traveling in miles per hour (mph)?

Answer 1

Answer: Approximately 1038 mph

The more accurate value is 1037.51097384802

Round that however you need to.

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Explanation:

We need the circumference of the equator. Think of the equator as the largest possible circle (or belt) to fit around the earth.

C = pi*d

C = pi*7926

C = 7926pi

C = 24,900.2633723527

In 24 hours, a person at the equator travels roughly 24,900.2633723527 miles since the earth does a full rotation in this timespan.

Divide the two quantities distance over time to get the speed

rate = distance/time

rate = (24,900.2633723527 miles)/(24 hours)

rate = ( (24,900.2633723527)/(24) ) miles per hour

rate = 1,037.51097384802

rate = 1038 mph

I'm rounding to 4 sig figs since the diameter is given to be in four sig figs.

This speed of roughly 1038 mph is a linear speed and not an angular speed.

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Extra info (optional section)

Upon further research, I found an article from NASA JPL (jet propulsion laboratory) which states quote:

"To make one complete rotation in 24 hours, a point near the equator of the Earth must move at close to 1000 miles per hour (1600 km/hr)"

Their figure of 1000 mph seems to be a rough estimate, more or less. It's fairly close to the 1038 figure we got earlier.