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That is not an appropriate towing attachment, with limited exception: IF your bumper has a load rating stamped on it, and has the reinforcement plates between the bumper and frame, then it'll be good for whatever the rating is (usually 300lb tongue weight, 3000lb max trailer weight). If the existing bumper does not have a stamp, or does not have reinforcement plates, then no go. Even if it is actually a towing bumper, it's still a poor substitute for an actual receiver hitch, and is opening you up to liability in case something goes wrong.
You can get a Reese frame-mounted receiver hitch from wal-mart for $120, it fits most Explorers, Rangers, and Sport-Trac.
X2. Look at your bumper. If it's similar to the '98 Explorer (and other years up and down the range) all you have is a 3/16s plate that fits inside the chrome outer bumper, which is only about two steps tougher than a gum wrapper.
The Explorer bumpers were rated for 3500lbs, 300 tongue iirc, and that info was printed on the plastic insert where the trailer hitch ball bolts on.
If you need more than that, get the reciever hitch as per prior post.
I still would be cautious of using that for a bike rack for two reasons- First, the bike rack will put a fair bit of torque on it, twisting it down, and second, if you sell the truck or someone borrows it down the road, they see a receiver and don't know it's limitations. That comes back into the liability end of things. It's only $120 to do it right.
Liability is something I never thought of, and a very good point. As for the $120, unfortunatly I live on a island off the west coast of Canada and shipping is a killer. I can't find one for under $250, which is steep to put a bike rack on. I think I will continue to look at the salvage yards for one, or bite the bullet.