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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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Slowly swipe from either end beginning with the white vertical bar to get an idea of the starting or ending digits. For less drama, just double click the answer area. The distance between the two bars will give you an idea of the magnitude. Touch devices can tap and hold the center of the box between the two bars and choose define to reveal the answer.
|1856532.8455|

#### 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