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## 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.

#### Analysis

$\frac{\pi(2gvh+v^3)^2}{4g^3}$

#### Project Euler 317 Solution

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#### Afterthoughts

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## Discussion

### 2 Responses to “Project Euler 317 Solution”

1. Never mind. I figured it out, although in a different manner.

Posted by Max Headroom | October 18, 2015, 6:30 AM
2. Could somebody please elaborate on that formula? How you came to think of it, or how it came to you? Thank you!

Posted by Max Headroom | July 31, 2015, 4:36 AM