## College Physics (4th Edition)

The gravitational field strength is $\frac{GM}{R^2}$, where $M$ is the Earth's mass, and $R$ is the distance from the center of the Earth. Let $R_E$ be the radius of the Earth (which is 6380 km). Let $h$ be the altitude above sea level. We can find $h$: $\frac{GM}{R_E^2} = 9.803~N/kg$ $\frac{GM}{(R_E+h)^2} = 9.792~N/kg$ We can divide the first equation by the second equation: $\frac{(R_E+h)^2}{R_E^2} = \frac{9.803~N/kg}{9.792~N/kg}$ $(R_E+h)^2 = \frac{9.803}{9.792}~R_E^2$ $R_E+h = \sqrt{\frac{9.803}{9.792}}~R_E$ $h = R_E~(\sqrt{\frac{9.803}{9.792}}-1)$ $h = (6380~km)~(\sqrt{\frac{9.803}{9.792}}-1)$ $h = 3.58~km$ The balloon is 3.58 km above sea level.