Aperson who weighs 800n on the earth's surface will weigh 200n at what height above the earth

6,400 km

Explanation:

The weight of a person is given by:

where m is the mass of the person and g is the acceleration due to gravity. While the mass does not depend on the height above the surface, the value of g does, following the formula:

where

G is the gravitational constant

M is the Earth's mass

r is the distance of the person from the Earth's center

The problem says that the person weighs 800 N at the Earth's surface, so when r=R (Earth's radius):

(1)

Now we want to find the height h above the surface at which the weight of the man is 200 N:

(2)

If we divide eq.(1) by eq.(2), we get

By solving the equation, we find:

which has two solutions:

--> negative solution, we can ignore it

--> this is our solution

Since the Earth's radius is , the person should be at above Earth's surface.

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