In 1495 European sailors discover america, and found the nasty surprise that dinosaurs had survived in this continent and are the dominant species.
Can an early arquebus kill or damage a large carnivore as a T-rex?
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The caliber of an arquebus could vary pretty widely but would typically fall somewhere between .69 to .80, had a muzzle velocity of around 1351 fps, and had a smooth bore.
To offer a comparison a modern 12 gauge shot gun is about a .748 caliber, 1800 fps, and also a smooth bore.
So to generalize an arquebus is a bit like a slow loading, less accurate, and slightly less powerful shotgun... Keep in mind that a 12 gauge slug is pretty formidable and you could probably get a slightly better comparison by looking at reduced recoil shells.
Here's a video with some pretty good ballistic gel analysis. You're likely to see a foot or more of penetration with a rather large residual cavity.
So what does this all mean for you?
Well, in a volley of fire formation which was typical for the arquebus, shooting at a t-Rex you're likely to strike it a few times. Each hit will likely mean a fairly deep traumatic wound and if nothing else some significant blood loss.
Would it stop a t-Rex charging toward you at 30mph? Probably not.
Would it eventually bleed out, or die from internal injuries? Probably.
Would it kill you before it bled out? Most likely.
What hope is there? Use cannons as well.
There were guns that ivory hunters used that could take down elephants, but they had to hit them in the heart because anywhere else wouldn't kill them, and they wouldn't penetrate the elephant's skull.
I guess if you found a weak spot then the same/similar gun could be used to kill a T-rex, but they're obviously a lot bigger.
Maybe if you sneaked up on it or distracted it and managed to shoot its Achilles tendon (no idea if dinosaurs have those, but if not then something similar) so that it would be unable to stand, then you could get another shot off into the heart once it's lay on the floor.
A lot depends on the dinosaur you are shooting. If they are the monsters most people associate with dinosaurs (T-rex, giant sauropods, ceratopsidae like the Triceratops etc.) then your best bet is to either stand very still or run very fast. If a Velociraptor pack sights you, then all bets are off.
The slow loading speed and limited power and accuracy of the firearms of the 1400's also means that you will have a difficult time trying to deal with many of the smaller dinosaurs, which would be very fast moving (with T-rex as the apex predator, they better be) and extremely hard to hit. In many cases, the crossbowmen might have a better chance of hitting the smaller dinosaurs, and a big crossbow quarrel would do considerable damage as well.
If you can land enough people in North America, then the military technology of the time might offer some help. Large formations like a Tercio use masses of pikes to protect the firearm wielding soldiers while they reload, and a bristling pike square might deter most of the lesser carnosaurs. If you can wait for the 1600's, Gustave Adolphus can come to the rescue with lightweight cannon that can move with mobile formations in the field, evening out the odds a bit more (and the musketry will also be somewhat more effective as well.
Individual soldiers in the 1400's could also be armed with various sorts of pole arms, which provided enough reach and leverage to crack open an armoured knight; this would also give them a chance against many types of dinosaur as well. Mounted knights probably won't do well (the horses would shy from the dinosaurs, and predators would simply see a mounted knight as lunch), but dismounted men at arms with full armour and pole arms or maybe a 2 handed sword would have protection and an effective weapon. Working with a formation of pikemen, arquebusers and crossbowmen, you would have a fighting chance in a dinosaur environment.
I did not include longbows since they were very specialized and only a very small number of Europeans were proficient with their use, mostly because the Welsh and English trained for a lifetime to use them effectively. Henry V could probably use his army of 5000 bowmen backed by men at arms to fend off dinosaurs until the arrows ran out.
Even modern firearms would be iffy, although the accuracy and firing sped would be vastly improved, you are still dealing with rather large targets which will need multiple hits (especially with smaller calibre firearms). When you go dinosaur hunting, you probably want a .416 Weatherby Magnum or a Barrett Light .50 instead.