EPT*Happy tears leaking*
Empyrean's Math Problem of the Day - Page 4
| Forum Index > General Forum |
|
HappyManRun
1111 Posts
*Happy tears leaking* | ||
|
HappyManRun
1111 Posts
| ||
Empyrean
17004 Posts
| ||
|
BigBalls
United States5354 Posts
problem 4 just looks annoying, ill give it a look later if i have some time | ||
|
Empyrean
17004 Posts
 Unless you guys are working  I'm pretty sure you can find day four on the internet somewhere. It was a past competition problem, so it should be posted somewhere. I don't even remember where I remember it from lol. | ||
|
Cambium
United States16368 Posts
IMO, this problem is pretty elegent and relatively simple, so GL. You have an object (of negligible size) that's being shot out with an initial horizontal velocity of 8 m/s (y velocity is 0 m/s). What is its acceleration at t = 0.25 s? What are its centripetal and tangential acceleration at this time? | ||
|
brian
United States9626 Posts
it would have no acceleration, except air resistance if it was just shot out of something.. centripetal would be 9.8 would it not? gravity..? i dont think i understand the question >.< | ||
|
brian
United States9626 Posts
| ||
|
Cambium
United States16368 Posts
On January 07 2006 20:39 Gene wrote: i dont think i understand the question >.< Uh.... you need a little physics background in order to solve the problem. y velocity is upward velocity? Ok, the initial y-velocity is 0 meaning that it's shot out straight out horizontally. it would have no acceleration, except air resistance if it was just shot out of something.. centripetal would be 9.8 would it not? gravity..? Gravity is a form of acceleration. No, the centripetal acceleration is not 9.8 ms^-2 | ||
|
brian
United States9626 Posts
in a frictionless environment(i.e. no air resistance) the horizontal velocity will remain constant, therefore no acceleration(horizontally), and the only force acting on said body will be the force of gravity, meaning the object will have an acceleration downwards of -9.8 m/s^2 :| but i understand now what it is, exactly, you are asking. and i dont quite remember the right forumlas ;| | ||
|
Cambium
United States16368 Posts
On January 07 2006 21:14 Gene wrote: i have a little physics background -_- in a frictionless environment(i.e. no air resistance) the horizontal velocity will remain constant, therefore no acceleration(horizontally), and the only force acting on said body will be the force of gravity, meaning the object will have an acceleration downwards of -9.8 m/s^2 :| but i understand now what it is, exactly, you are asking. and i dont quite remember the right forumlas ;| Ok, it will only have a vertical acceleration, that is correct. So I guess you got the first part right. However, in this case, there are two components that add up to g, and that is what the question is asking for - its centripetal acceleration (because the falling motion of the object will trace a parabola) and its tangential acceleration (the acceleration that is tangent to the curve at t=0.25s). | ||
|
brian
United States9626 Posts
| ||
|
Cambium
United States16368 Posts
You'll most definitely need calculus to solve this. | ||
|
brian
United States9626 Posts
| ||
|
wastoid
United States47 Posts
On December 17 2005 18:20 LastWish wrote: Ok I've got it! Catyouls solution is eventually right. heh, I tried to solve it computationally and came sorta close at 24800 ;P I'm only mentioning it because there were some interesting patterns that I saw to while trying to get that 24800 projection. One interesting thing is that for any N>0 number of zeroes, there are only five numbers that end in N zeroes. The other was that there was an interesting pattern in how the number of zeroes increased: it would increase by 1 every 5 numbers, but after 6 times of increasing this way, it would always skip a number the number of zeroes would increase by 2 instead of 1. So the skipped numbers were 5, 11, 17, 23, 29.. (skip), 30, 36, 42, 48, 54, 60.. (skip), 61, 67, 73, 79, 85, 91... (skip) etc Anyway, just thought it was a cool pattern. I don't mean to tarnish the the elegance of the pure math presented here; I wish I coulda figured it out that way myself.  I was hoping that by analyzing this stuff that I'd get some insight, but alas it didn't. I did all this in Python if anyone is curious about it; support for long integers is pretty good so computing the larger numbers for testing wasn't so bad. | ||
| ||
