A man is hovering above a Schwarzschild black hole. He is 1 meter tall. What would be the radius of the black hole if the man's head is accelerating away from his feet at a rate of 10 m/s^2.
The Attempt at a Solution
The force on the man would be equal to GMm/r^2, where M is the black hole mass and m is the man's mass and r is the Schwarzschild radius. This means the acceleration is GM/r^2 ... but I've hit a snag.