Answer:
\(355.8km\)
Explanation:
We use the equation to calculate gravitational acceleration \(g\)
\(g=\frac{GM}{r^2}\)
where is the universal gravitational constant \(G=6.67x10^{-11}m^3/kgs^2\), \(M\) is the mass of the earth: \(M=5.97x10^{24}kg\), and \(r\) is the radius from the center of earth.
Clearing for the distance r:
\(r=\sqrt{\frac{GM}{g} }\)
substituting known values
\(r=\sqrt{\frac{(6.67x10^{-11}m^3/kgs^2)(5.97x10^{24}kg)}{8.80m/s^2} }\)
\(r=\sqrt{\frac{3.982^{14}m^3/s^2}{8.80m/s^2} }\)
\(r=\sqrt{4.525x10^{13}m^2 }\)
\(r=6.7268x10^6m\)
and since the radius of earth from the core to the surface is about \(6.371x10^6m\), the distance above the surface where g is reduce to \(8.80m/s^2\) is:
\(r=6.7268x10^6m-6.371x10^6m=355,800m\) wich in kilometers is: \(355.8km\)
