Project Euler 317: Find the volume of the airburst region of a firecracker detonation.
Problem Description
A firecracker explodes at a height of 100 m above level ground. It breaks into a large number of very small fragments, which move in every direction; all of them have the same initial velocity of 20 m/s.
We assume that the fragments move without air resistance, in a uniform gravitational field with g=9.81 m/s^{2}.
Find the volume (in m^{3}) of the region through which the fragments move before reaching the ground.
Give your answer rounded to four decimal places.
Analysis
Project Euler 317 Solution
Runs < 0.001 seconds in Python 2.7.Use this link to get the Project Euler 317 Solution Python 2.7 source.
Afterthoughts

No afterthoughts yet.
Never mind. I figured it out, although in a different manner.
Could somebody please elaborate on that formula? How you came to think of it, or how it came to you? Thank you!