Problem 317

amlesh44 · Post by **amlesh44** » Sun Jan 02, 2011 3:49 am

For this question, can we assume that the firecracker exploded on earth? If so, since earth isn't perfectly spherical, it matters where on earth the firecracker exploded. So, what should we assume?

TripleM · Post by **TripleM** » Sun Jan 02, 2011 4:10 am

A firecracker explodes at a height of 100 m above level ground... in a uniform gravitational field with g=9.81 m/s^(2).

All assumptions are provided in the problem.

amlesh44 · Post by **amlesh44** » Sun Jan 02, 2011 5:22 am

Ah, thanks TripleM. Seems that I didn't read the problem statement intently enough.

x10 · Post by **x10** » Sun Jan 02, 2011 12:48 pm

Hello, I believe I have solved the problem, but I'm getting a wrong answer.
I believe it's an error from rounding, because I figured out a formula for the solution volume(as a solid) and tested it by overlaying graphics of my formula and the "brute-forced" parametrized equation of the solid composed of all the firework particles. They seem to match pixel for pixel(i.e. my solution seems to at least be close to the answer).

Can someone who has solved 317 please PM me and confirm if I have a rounding error? I'll send my graphs, equations & answer

swatcher · Post by **swatcher** » Mon Jan 03, 2011 8:42 am

I am in a similar situation - I haven't modelled my result but I am very confident in it, except for the precision. Would someone PM me so I can check my result?

TripleM · Post by **TripleM** » Mon Jan 03, 2011 9:48 am

You can both PM me, but I wouldn't think a precision error would be that likely.

x10 · Post by **x10** » Mon Jan 03, 2011 11:05 am

Yes, I can agree that a precision error is unlikely, because the rounding isn't anything special(i.e. the answer isn't X.100099999)

My error was that I had actually forgotten a certain formula and my recollection from memory lacked a certain term. I.e. my answer was (about) half of the real answer.

So, yeah, double-check your formulas and when in doubt - use Wikipedia, even for the really really simple things

joho · Post by **joho** » Tue Jan 04, 2011 8:55 pm

So is it the volume the fragments move through before some fragment reaches the ground or the volume the fragments move through before all fragments reaches the ground which should be computed?

TripleM · Post by **TripleM** » Tue Jan 04, 2011 9:23 pm

Any point that any fragment passes through should be included in the volume.

raggie · Post by **raggie** » Mon Jan 10, 2011 12:18 pm

double check

Used 10 instaed of 9.81 in my maths, that's probably what's going wrong

browni3141 · Post by **browni3141** » Fri Mar 04, 2011 11:22 pm

Hello, I did this problem with pencil/paper and figured the final anwer with my TI-83. I think there's a chance I lost accuracy by using the calculator. I think my method is correct, but I made one assumption in my calculus. That could also be the problem. Could I pm someone to see if my answer is close?

Edit: Nevermind, I never covered how to find the volume of a surface of revolution in high school. Anyway, I figured it out on my own. Very fun problem.

Edit Again: See my forum post for a generic formula.

Also, could someone tell me how to get symbols like pi and theta in my posts?

kapila_619 · Post by **kapila_619** » Thu Jul 07, 2011 9:38 am

I am stuck in the math of this problem

I have solved it using normal math(volume of solid of revolution) and physics(equations of motion) but I am getting wrong answer

please can anyone see my solution and tell me where I have gone wrong

I am getting answer as

Expand

JiminP · Post by **JiminP** » Mon Nov 07, 2011 2:19 pm

I got the fomula

Expand

and result

Expand

but I was wrong.

Where's my problem? I can send you my pdf file which I wrote how above formula is made.

matthewden · Post by **matthewden** » Tue Dec 06, 2011 8:44 pm

Can I get some clarification on a few things?

Is air resistance something I need to take into account in this problem?
And a slightly silly question: Does "It breaks into a large number of very small fragments, which move in every direction" (from the problem statement) mean that some of the particles will travel up? I would assume no, but just want to make sure...

Thanks!

Marcus_Andrews · Post by **Marcus_Andrews** » Tue Dec 06, 2011 8:49 pm

matthewden:

1. From the problem description:

We assume that the fragments move without air resistance...

2. The fragments move in every direction, including straight up.

matthewden · Post by **matthewden** » Tue Dec 06, 2011 8:59 pm

Oh, yeah. It does say that.... OK. Thank you.

mdean · Post by **mdean** » Mon Jul 08, 2013 9:36 am

Ugh... So far, this problem has been a lot of ugly pencil and paper math. I hope I get this right the first time, because I am not going to want to comb back through it looking for a mistake.

I think I'm about one step away from solving this, but I see one interesting result which I have yet to determine whether or not it makes sense.

Update: crap... I'm hoping this is just going to be a simple mistake. I get the feeling my value isn't off by much.

mdean · Post by **mdean** » Mon Jul 08, 2013 11:11 am

And it looks like everything is checking out. Not sure what to do at this point. As far as I can tell, I should have a correct answer. I'm stumped.

Update: Never mind. Good old unit checks on physics problems. Problem completed.

golfguy37 · Post by **golfguy37** » Tue Jul 23, 2013 11:47 pm

If two particles pass through the same point in space, should that point be counted twice in the total volume calculation?

Marcus_Andrews · Post by **Marcus_Andrews** » Wed Jul 24, 2013 12:13 am

No, because the question is asking for the volume of the region through which the fragments move.

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