Question

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

A) How long does it take for it to rotate 310 degrees?

B) How long does it take to rotate 5 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.

Answer 1

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

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.

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° =
`(24)/(360)` hours.

Time taken by earth to rotate 310° =
`(24)/(360)*310` 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 =
`(24)/(2\pi)` hours.

Time taken by earth to rotate 5 =
`(24)/(2\pi)*5` 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\:=(360)/(24)*2=30^(\circ)`

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

Length of the Arc =
`(\theta)/(360)*2\pi r`

Length a point on equator moves in 2 hour =
`(\theta)/(360)*2\pi r=(30)/(360)*2*3.14*3960=2072.4\:miles`