Project Euler 317: Find the volume of the air-burst 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/s2.
Find the volume (in m3) 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
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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!