"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.