Final answer:
The Schwarzschild radius if the Milky Way collapsed into a black hole would be about one-tenth of a light year, much smaller than the galaxy's size and our distance from its center. The escape speed from the surface of Mercury is approximately 4.25 km/s.
Step-by-step explanation:
Schwarzschild Radius of the Milky Way
If our Milky Way galaxy, which is comprised of about 100 billion stars, were to collapse into a black hole, its Schwarzschild radius would be approximately one-tenth of a light year (about 1012 kilometers). This radius is significantly smaller compared to the Milky Way's actual size. When we relate this Schwarzschild radius to our distance from the center of the galaxy, which is about 27,000 light years, we find that the black hole's event horizon would be an extremely small point compared to the vast scale of the galaxy.
Escape Speed from Mercury;
The escape speed of a projectile from the surface of Mercury can be found using the formula v = \( \sqrt{2GM/R} \), where G is the gravitational constant, M is the mass of Mercury, and R is the radius of Mercury. Using the standard values for these variables, the escape speed from Mercury would be approximately 4.25 km/s.