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A satellite in a circular orbit rotates around the Earth every 120 min

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A satellite in a circular orbit rotates around the Earth every 120 min  [#permalink]

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New post 03 Aug 2019, 23:05
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B
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  45% (medium)

Question Stats:

50% (01:44) correct 50% (02:39) wrong based on 30 sessions

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A satellite in a circular orbit rotates around the Earth every 120 minutes. If the Earth’s radius is 4000 miles at sea level, and the satellite’s orbit is 400 miles above sea level, approximately what distance does the satellite travel in 40 minutes?

A. 1400 miles
B. 9210 miles
C. 4400 miles
D. 4120 miles
E. 8000 miles

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Re: A satellite in a circular orbit rotates around the Earth every 120 min  [#permalink]

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New post 05 Aug 2019, 10:33
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Top Contributor
SajjadAhmad wrote:
A satellite in a circular orbit rotates around the Earth every 120 minutes. If the Earth’s radius is 4000 miles at sea level, and the satellite’s orbit is 400 miles above sea level, approximately what distance does the satellite travel in 40 minutes?

A. 1400 miles
B. 9210 miles
C. 4400 miles
D. 4120 miles
E. 8000 miles

TPR


This diagram might help
Image

So, the black dot represents the Earth's center.
So, the radius of the satellite's orbit = 4400 miles

circumference of circle = 2πr

So, the circumference of satellite's orbit = 2π(4400) = 8800π

GIVEN: the satellite in a circular orbit rotates around the Earth every 120 minutes.
In other words, the satellite travels 8800π every 120 minutes

So, in 40 minutes, the satellite will travel 1/3 of the 8800π mile orbit (since 40 minutes is 1/3 of 120 minute)

Distance traveled = 8800π/3

PRO TIP: Since π ≈ 3.14, we know that π/3 ≈ 3.14/3 ≈ some number a little bit bigger than 1

So, 8800π/3 = 8800(π/3) = 8800(a number a little bit bigger than 1) = some number a little bit bigger than 8800

Answer: B

Cheers,
Brent
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Re: A satellite in a circular orbit rotates around the Earth every 120 min   [#permalink] 05 Aug 2019, 10:33
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