Erm... Perhaps I am lazy, but I would go with the Wikipedia statement about this (that of course could be wrong) and call it a day.
That would imply:

• It went 21mi up, that is 33Km in human units.
• A passenger plane (747, etc.) normally flies at around 9-10km (TBH, almost always I've flown it rarely higher than that, 40,000 ft is too high IMHO)
• Conclusion: It went up three times higher than a passenger plane.

 

i have another site open that states otherwise
http://www.britishmuseum.org/whats_...rculaneum/pompeii_live/eruption_timeline.aspx

also i would like the info to be as accurcate as possible as my family has a very rich and close bond to pompeii

 

it ust did a random google search ad 39k ft came up twice

 

I just really want to nail this project as there is a good price for 1st place and that i am also related to the guy that found it.... DEADASS

 

"good price for 1st place"
If your attitude to the project was conveyed in this thread then good luck with that. In most schools of any reasonable size there is usually someone quite bored that will go all in.

If your profile is accurate and you are 14 it changes the requirements a bit compared to some other ages and skill sets, however you don't have to be limited to what they teach you (unless you are being examined on what they teach you in which case most lesser places, which is most of the world, will penalise you for colouring outside the proverbial lines, even if that is what physics says).

Start with.

How do they tell today? Got atmospheric probes I imagine. Lacked those 2000 years ago though and time travel has not yet been invented.

The atmosphere was mostly the same though so you can use secondary indicators. The higher you go, the different wind systems you interact with and the further it goes.
Can you then dig down in sediment around the world to see what went on? Ice cores are a similar field in this instance.
Was it big enough to do one of those temperature drops, something that will be indicated in plant growth rings? Alternatively http://mentalfloss.com/article/29879/6-oldest-trees-world
Would blast damage (something not without documentation here) and resulting conditions allow estimation of the energy and thus able to be compared or extrapolated from a known event from modern times or with more documentation?

You need not be limited to one of those either -- a combined model is often a better one.

 

... then do it?
Nobody prevents you from taking a look into good old encyclopedia Britannica, and then further into the source of each citation, like we did back in my days.

 

I can't imagine a teacher is going to pass an assignment with no references, or give a score much above a bare pass on one with only Wikipedia and the like references. But if course I remember that the quality of schooling in the US is not very high so maybe they don't teach you to reference at all. When I was at school, a quote from a book or website without giving the source was an automatic fail and referal to the principal (plagiarism), and no references at all was a probable fail unless the quality of the writing was very high.