[A]ssuming you were stupid enough to sneak up under a T. rex and pull the cloaca open, the last thing you would ever see during the last moments of your life would be a penis if it was a male, probably similar to that seen in a crocodile.”
That's quite an image. Now that some of you are shaking your head in puzzlement, I'll explain why this is interesting.
It's easy to forget that dinosaurs were real animals. They were born (or hatched), grew from juveniles into adults, wandered around the landscape, ate, slept, pooped, and had sex (just like most of us).
Dinosaurs, of course, are known to us because of their fossil bones preserved in Mesozoic Era sedimentary rock strata. While we can obtain a lot of information from these bones, as well as some other types of trace fossils such as trackways, there is still a lot they can't directly tell us about the animals themselves. Those of us fascinated by dinosaurs also want to know the details of what they looked like (what color were they, for example) and how they behaved. Some paleontologists are even interested in how dinosaurs had sex (as the joke about porcupine sex goes, "very carefully").
One very basic question is whether or not dinosaurs (the males ones) had penises. We know that the group of reptiles we call dinosaurs evolved from an earlier group of reptiles called archosaurs. Another group of reptiles evolved from the archosaurs as well and they're still around - the crocodilians. We also know that birds evolved from one of the lineages of dinosaurs.
Crocodiles and birds create what paleontologists call an extant phylogenetic bracket for the dinosaurs. What this means is that whatever characteristics are present in both crocodiles and birds were probably also present in the dinosaurs as well.
Well, maybe not. Some birds (like male ostriches, cassowaries, kiwi, geese, and some species of swans and ducks), for example, actually have a penis which is used for reproduction. All of the bird groups which exhibit a penis are lineages near the base of the bird family tree. It appears to be an ancestral feature.
It also turns out crocodilians have a form of penis inside their cloaca as well (not well studied, surprisingly enough).
Given this, dinosaurs very likely had a penis inside their cloaca. After watching the video above, I'm not sure I'd want to be too close to a T. rex's cloaca.