Fun With Math

[webshark3]

OK, story problem time.

I want to be able to shoot all the way down the length of a 100 yard soccer field with my 1.6 crop Canon camera and have my 5ft son fill at least 2/3 of the frame in normal landscape orientation. At the same time, another train leaves Seattle going 85mph carrying a guy with a Nikon....

The question is, what is the cheapest lens that will let me do that with a reaonable amount of IQ. I already have a 1.4x extender and want a lens that will still autofocus (app = f/5.6).

You are not required to show your work to get credit but if you can talk my wife into getting me the lens for father's day you get double points!

Can I show by example?

This is a 100% crop from my Sigma. 28mm wide angle at f4. It's a APS-C sensor with a 1.7x crop factor.

So I guess my short answer is that you can get good IQ with a DSLR and long glass, or wide good glass and crop, or a small sensor P&S with good zoom.