2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								id: 5900f4aa1000cf542c50ffbc
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								challengeType: 5
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								title: 'Problem 317: Firecracker'
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								## Description
 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< section  id = '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.
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								Find the volume (in m3) of the region through which the fragments move before reaching the ground.
							 
						 
					
						
							
								
									
										
										
										
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								Give your answer rounded to four decimal places.
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								## Instructions
 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< section  id = 'instructions' > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								## Tests
 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< section  id = 'tests' > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								```yml
							 
						 
					
						
							
								
									
										
										
										
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								tests:
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								  -  text: < code > euler317()</ code >  should return 1856532.8455.
							 
						 
					
						
							
								
									
										
										
										
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								    testString: assert.strictEqual(euler317(), 1856532.8455, '< code > euler317()< / code >  should return 1856532.8455.');
							 
						 
					
						
							
								
									
										
										
										
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								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								## Challenge Seed
 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< section  id = 'challengeSeed' > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  id = 'js-seed' > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								function euler317() {
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								  // Good luck!
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								  return true;
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								euler317();
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								## Solution
 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< section  id = 'solution' > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								// solution required
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / section >