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Answer :
Answer:
45.95 pounds is the weight of the astronaut 4050 miles above the Earth.
Step-by-step explanation:
The gravitational force F ∝ [tex]\frac{1}{r^{2} }[/tex]
F = [tex]\frac{k}{r^{2}}[/tex]
where r = Distance of the object from the center of the earth
and k = proportionality constant
For the astronaut weight = 186 pounds
186 = [tex]\frac{k}{4000^{2}}[/tex] [ where radius of the Earth = 4000 miles]
k = [tex]186\times 16\times 10^{6}[/tex]
= [tex]2976\times 10^{6}[/tex]
If the object is 4050 miles above the Earth then the weight of the object will be F = [tex]\frac{2976\times 10^{6} }{(4000+4050)^{2}}[/tex]
F = [tex]\frac{2976\times 10^{6} }{(8050)^{2}}[/tex]
F = [tex]\frac{2976\times 10^{6} }{64802500}[/tex]
= [tex]\frac{2976000000}{64802500}[/tex]
= 45.94 pounds
Therefore, 45.95 pounds is the weight of the astronaut 4050 miles above the Earth.
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