Answer: Approximately 1038 mph
The more accurate value is 1037.51097384802
Round that however you need to.
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Step-by-step 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.