Can someone explain this physics question to me?

Question

As the earth rotates through one revolution, a person standing on the equator traces out a circular path whose radius is equal to the radius of the earth (6.38 106 m). What is the average speed of this person in meters per second and miles per hour?

i need not just the answer but a step by step please?

thanksies

Answer 1

To get the speed, you need to find the total distance the person traveled, the total time it took, and divide them.

To get the total distance, notice that the person is traveling around the circumference of a circle; so the circumference is the distance you want.  Use the standard formula: circumference = 2π × radius.

The total time, is the time it takes for the earth to rotate once; which of course is 24 hours.

To get the speed in meters per second, convert 24 hrs to seconds, and then divide distance by time.

To get the speed in mph, convert the circumference from meters to miles, and then divide distance by time.

Answer 2

His motion is a circular motion with angular velocity

ω = 2π/86,400 radian/second (1day = 86,400 seconds)

Relation between angular and linear speeds:

v = ωR = 2πR / 86,400

v = 2π 6.38 x 10^6 / 86.4 x 10^3 = 0.464 x 10^3 = 464 m/s = 1,670 km/h

Answer 3

The circumference of the earth is πd = 40.1e6 m and that is traced out every 24 hours, or 24*3600 seconds

So 40.1e6 / 24*3600 = 464 m/s

464 m/s x 1 mi/1609m x 3600s/hr = 1038 mph

.

Answer 4

speed = distance / time

distance = 2 pi  6.38*10^6 m = 40074784.2 meters =  24 901.3164 miles

time = 24 hours = 86400  seconds

mph => 24 901.3164/24 = 1037.55485 mph

m/s => 40074784.2/86400 = 463.828521  m/s