Question

The Earth completely rotates on its axis once every 24 hours.

Answer 1

Answer:

i dont know the other answers but the earth takes 4 mins to turn a degree so you multiply 310 by four then divide your answer by 60 to convert the answer from minutes to hours

Answer 2

Answer:

Part A). 20 hours 42 minutes taken by earth to rotate 310°.

Part B). 19 hours 6 minutes taken by earth to rotate 5 radians.

Part C). 2072.4 miles a point on the equator rotate in 2 hours.

Step-by-step explanation:

Given : Earth rotate 360° in 24 hours.

Part A).

Time taken by earth to rotate 360° = 24 hours.

Time taken by earth to rotate 1° = $\frac{24}{360}$ hours.

Time taken by earth to rotate 310° = $\frac{24}{360}\times310$ hours.

                                                   = 20.7 hours = 20 hours 42 minutes (approx.)

Part B).

Time taken by earth to rotate 360° = 24 hours.

We know that 360° = 2π radian

Time taken by earth to rotate 2π radian = 24 hours.

Time taken by earth to rotate 1 radian = $\frac{24}{2\pi}$ hours.

Time taken by earth to rotate 5 = $\frac{24}{2\pi}\times5$ hours.

                                                  = 19.098 hours = 19 hours 6 minutes (approx.)

Part C).

Diameter of Earth = 7920 miles

Radius of Earth, r  = 7920/2 = 3960 miles.

Degree of rotation in 24 hour = 360°

Degree of rotation in 2 hour, $\theta\:=\frac{360}{24}\times2=30^{\circ}$

Now use Formula used to calculate Length of the arc of the circle.

Length of the Arc = $\frac{\theta}{360}\times2\pi r$

Length a point on equator moves in 2 hour =  $\frac{\theta}{360}\times2\pi r=\frac{30}{360}\times2\times3.14\times3960=2072.4\:miles$