Miniature black holes. Left over from the big-bang beginning of the uniberse, tiny black holes might still wander through the universe. If one with a mass of `5.0 xx 10^11 kg` (and a radius of only `5.0 xx 10^(-16)m`) reached Earth, at what distance from your head would its gravitational pull on you match that of Earth's?

Explanation

To solve the problem of finding the distance from your head where the gravitational pull of a miniature black hole matches that of Earth, we can follow these steps:

### Step 1: Understand the gravitational force equations

The gravitational force exerted by Earth on an object of mass \( m \) at a distance \( R \) from the center of Earth is given by:

\[
F_{\text{Earth}} = \frac{G M_{\text{Earth}} m}{R^2}
...