Since we finally have snow and I plan on going out sledding to maintain some sort of sanity through midterm week, I thought I'd go over some of the basic physics involved.
In a way it's kind of like those ramp problems that we've seen far too many times with a block sliding down it. I usually enjoy building a jump about 3/4 of the way down the hill, where I will have reached a high velocity. This allows me the greatest X and Y displacement which I could indeed calculate if I measured how far I landed from it and how long I was airborne (if you're lucky you'll get maybe a second or two). Some factors that can affect this speed that you get are essentially the things that reduce drag and friction. If you get low on your chest that will reduce the drag force of air resistance because there is less of a surface area for the air to hit (F = -bAv). Also if you use a longer plastic sled you will probably get more friction than if you used a chest-style sled with a waxed bottom and this will give you a lower velocity. All of these things must be considered when attempting to achieve maximum airtime.