I suppose if you can have a couple of lions, some grizzlies and dire wolves on the Ark, the smaller dinosaurs wouldn't be much of an issue.
The issue is feeding all of those animals for 40 days and 40 nights. And what happens when the rains end and the floods recede? 40 days covered in water would have killed all of the plants on the planet. And, what are the predators supposed to eat post-flood if there are only two of each herbivore species left? As soon as the T-Rex eats one of the elephants, that's it for that species.
Double check your Genesis. It rained for 40 days and nights, then the Ark floated for 5 months. They entered on the seventeeth day of second month, and it landed on Mount Ararat on the seventeenth day of the seventh month.
As to what the animals ate, well, the Bible says that Noah and his three sons and their families all entered the Ark. It didn't say they all got off at the end.