Domain Not Resolving to Forwarded IP

I've recently registered a domain name with GoDaddy.com and forwarded it to my web server's IP address. Now when I enter the domain name in my browser, my site appears as expected.

The strange part is, when I ping the domain name, another IP address appears. Is this normal? I would expect it to resolve to my web server's address. Is there anyway to make it resolve that way?

If you require the registrar (godaddy) to forward your domain, godaddy will redirect the web access from a domain to your IP.

Client ===> Godaddy ===> You

Godaddy acts as an intermediate between the client and you.

If you want to bypass godaddy, the client has to initially resolve your domain as your IP. So the change must occur at the DNS level.

If godaddy takes care of resolving your domain (and subdomains), as it is likely to be, you have to edit your DNS settings with the Godaddy interface.
Edit the A field for @ (your domain name) and for www for instance (www.domain.name) that have to point to your IP address.

See Adding or Edit A records in the Godaddy help.