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03 Aug 2019, 23:05
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
60% (02:04) correct
40%
(02:20)
wrong
based on 134
sessions
History
Date
Time
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Not Attempted Yet
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
A. 1400 miles
B. 9210 miles
C. 4400 miles
D. 4120 miles
E. 8000 miles
Source: Test Prep Review
05 Aug 2019, 10:33
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SajjadAhmad
This diagram might help
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
23 Mar 2020, 00:13
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SajjadAhmad
Solution:
- • In 120 minutes satellite complete 1 rotation
- o In 1 minutes, satellite will cover \(\frac{1}{120}\) part of one rotation.
o In 40 minutes, stellite will cover \(\frac{1}{120}*40 = \frac{1}{3}\) part of one revolution
• Distance travelled in one rotation = circumference of orbit= 2*π*r
• \(\frac{1}{3}\)rd distance of 1 rotation = \(\frac{1}{3}*2* π*r\) =\(\frac{1}{3}*2*3.14*4400 =\frac{3.14}{3}*8800\) miles (approx.)
• The final answer is more than 8800, the only answer option more than 8800 is 9210
