He earth completely rotates on its axis once every 24 hours.
a) how long does it take for it to rotate 290 degrees?
b) how long does it take to rotate 7π radians?
c) the diameter of the earth is approximately 7920 miles. how far will a point on the equator rotate in 2 hours?
show all work. give answers to the nearest hundredth. include the units in your response.

A)

58/3 = 19.33 hours

B)

84.00 hours

C)

2074.29 miles

Step-by-step explanation:

Under the assumption the earth is a perfect circle, then in a complete rotation ( 24 hours) the earth will rotate through  360 degrees or 2π radians.

A)

In one day or 24 hours the earth rotates through 360 degrees. We are required to determine the duration it takes to rotate through 290 degrees. Let x be the duration it takes the earth to rotate through 290 degrees, then the following proportions hold;

(24/360) = (x/290)

solving for x;

x = (24/360) * 290 = 58/3 = 19.33 hours

B)

In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it will takes the Earth to rotate through 7π radians. Let x be the duration it takes the earth to rotate through 7π radians, then the following proportions hold;

(24/2π radians) = (x/7π radians)

Solving for x;

x = (24/2π radians)*7π radians = 84 hours

C)

If the diameter of the earth is 7920 miles, then in a day or 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle;

circumference = 2*π*R = π*D

                         = 7920*3.142

                         = 24891.43 miles

Therefore a point on the equator covers a distance of 24891.43 miles in 24 hours. This will imply that the speed of the earth is approximately;

(24891.43miles)/(24 hours) = 1037.14 miles/hr

The distance covered by the point in 2 hours will thus be;

1037.14 * 2 = 2074.29 miles

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step-by-step explanation: