I want to be able to zoom in on things 100 yards out?

I want to be able to zoom in during my son's sporting events for close up shots approx 100 yds out what lens should i be looking at, have nikon d3100 SLR… Thanks

The most affordable option in my opinion is the Nikon 70-300mm f/4.5-5.6

http://www.nikonusa.com/...IF-ED.html

You get the long reach of 300mm during the game. You have VR technology, so you don't need to rely on a tripod. Assuming your son is playing outdoors during the daylight (not indoors or at night) you will have enough light to use it at f/5.6. Also, for a lens of this focal length, it is relatively small.

Alternatively:
The more expensive and ideal option that is the standard for most professionals. 70-200mm F/2.8
But it is much more expensive, and it doesn't reach as far.

While not a great lens, the Nikon 70-300 (?$) or the Sigma 70-300 (around 400$) are probably your best bet.

If you have tons of money you could get yourself the 70-200 f2.8 (2600$). That lens, while not having the same reach, has MUCH better optics and can open much wider meaning they are better for low light conditions or to have a nice blurry background while your subject is in focus.

This shot was done with the 70-200 f2.8 L series from Canon on a Rebel T1i.

Notice how the subject (the groom) is in focus while the foreground and backgrounds are nice and blurry.

I also own the 70-300 Sigma lens and it basically sits there gathering dust. I carry it in my walkaround kit mainly because I don't own the 70-200 yet.It. Ok when there's decent light but nothing compared to the 70-200 L series.