SOLUTION: The weight of an object varies inversely as the square of its distance from the center of the earth. The radius of the earth is 6400 km, if a man is 80 kg on the earth‘s surface,
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Question 1162178: The weight of an object varies inversely as the square of its distance from the center of the earth. The radius of the earth is 6400 km, if a man is 80 kg on the earth‘s surface, what will he weigh 2000 km above the earth? 4000 km above the earth?
Based on the problem condition, you can write the inverse proportion
= = = 0.58.
From this proportion, the weight of the 80 kg person at the height of 2000 km above the Earth surface is
x = 0.58*80 = 46.4 kg.
Solved.
Using this solution as your TEMPLATE, you can solve the second problem ON YOUR OWN.
Happy calculations (!)
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The post-solution note.
Starting from 60-ies of the last century, kilograms are not used as a unit for weight (and for force).
It was replaced by N (newtons). 1 kg (force) = 9.81 N (newtons).
You can put this solution on YOUR website! w=k/d^2
80=k/6400^2
k=3,276,800,000
at 2000 km above, r=8400^2
so weight is 3276800000/8400^2=46.44 kg
at 4000 km above r=10400 km, so weight=30.296 or 30.30 kg.
Simpler is that the ratio of the weight on Earth to 2000 km above earth is (6400/8400)^2=0.5805, and that *80 is 46.44 kg.
