Answer
$R_B=0.8m$
Work Step by Step
The distance of black hole $R_B$ can be determined through the following steps:
1-The two gravitational forces must be equal for the given condition. That is,
$\frac{Gm_{person}M_E}{R_E^2}=\frac{Gm_{person}M_B}{R_B^2}$
Where $m_{person}$, $M_E$, $M_B$,$R_E$, $R_B$ are the mass of person, mass of Earth,
mass of black hole, radius of Earth and radius of black hole respectively
2-After simplification, we obtain:
$\frac{M_E}{R_E^2}=\frac{M_B}{R_B^2}$
3-$R_B=R_E\sqrt{\frac{M_B}{M_E}}$
4-We plug in the known values to obtain:
$R_B=6.4\times 10^6\sqrt{\frac{1\times 10^{11}}{5.97\times 10^{24}}}$
$R_B=0.8m$
