IMAGINE- a building 6400km. high. On the ground floor, a person weighs 175lbs when he steps on a spring scale how much would the man weigh on the same scale if he were standing at the top floor? HINT: Note that 6400km is also the radius of the earth so that the top floor is 2Re from the earths center. Think about what this means for Fgrav before you start plugging in numbers or making conversions

Answer 1

I KNOW THIS MUCH----- confuesed what to plug in where. and what not to plug in. The weight is equal ‘mg”
On the Earth surface acceleration due to gravity is
mg=GmM/R²,
g=G•M•/R²,
where
the gravitational constant G =6.67•10^-11 N•m²/kg²,
Earth’s mass is M = 5.97•10^24 kg,
Earth’s radius is R = 6.378•10^6 m.
g=9.8 m/s²

Let's find “g” at the height “h” . Distance between the mas “m” (the person) and the center of the Earth is 2R =>
m•g1= G•m•M/(2R)²
g1= G•M/4R²=g/4

In the "high" building mg1= mg/4

Answer 2

You are making this much too complicated.
This is right:
mg=GmM/R²

now what if to went to radius = 2R
then
mg = GmM/(2R)^2
= GmM/4R^2
or
new weight = 1/4 of original weight

Answer 3

That is what their HINT means.