A spaceship that is traveling 3,600 kilometers per hour can make a cir : Problem Solving (PS)

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A spaceship that is traveling 3,600 kilometers per hour can make a cir

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Math Expert

Joined: 02 Sep 2009

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A spaceship that is traveling 3,600 kilometers per hour can make a cir [#permalink]

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07 Sep 2018, 00:06

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Difficulty:

45% (medium)

Question Stats:

63% (01:59) correct

38% (01:59) wrong

based on 42 sessions

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A spaceship that is traveling 3,600 kilometers per hour can make a circular orbit around a spherical planet in 4 minutes. Approximately how far is the spaceship from the center of the planet?

A. 12,000 kilometers
B. 1200 kilometers
C. 240 kilometers
D. 120 kilometers
E. 40 kilometers

Spoiler: OA

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ISB, NUS, NTU Moderator

Joined: 11 Aug 2016

Posts: 376

Re: A spaceship that is traveling 3,600 kilometers per hour can make a cir [#permalink]

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07 Sep 2018, 02:37

Bunuel wrote:

let the spaceship be h kms above the centre of the planet.
To complete 1 orbit it will have to travel 2*\pi*r.

total distance travelled = speed *time
=\(3600*\frac{4}{60}\)
=\(2400 km\)

\(240=2*\pi*h\)
therefore, \(h= \frac{240}{(2*3.14)}\)
approximating 3.14 as 3 because answer choices are multiples of 10.
h=40 km

Answer: E
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Re: A spaceship that is traveling 3,600 kilometers per hour can make a cir [#permalink]

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09 Sep 2018, 01:07

Bunuel wrote:

Speed= 3600 km/hr = 3600/60 = 60 km/min
In 4min, the spaceship covers a distance of 60 x 4 = 240 km
The circumference of the rotational path of the spaceship is 240 km
Distance of spaceship from the center of planet (Radius) = \(\frac{240}{{2π}}\)
π=3.14~3 (Since the question asks approximately)
Distance = \(\frac{240}{{2*3}}\)=\(\frac{240}{6}=40\)
Answer E.
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