Typically bullets have muzzle energy in the order of 10^3 (thousands) of NM. So say the most powerful handguns have around 1200NM of muzzle energy. A 50 cal anti-materiel rifle might ready 10^4 (tens of thousands, say 15000) NM.
Typically a powerful conventional (say hunting) bow might produce 10^2 (hundreds) NM of kinetic energy. So a powerful handgun is sort of 10 times more powerful than a hunting bow. A powerful rifle a hundred times.
Could we make a bow 100 times more powerful than they are now using modern materials (ignoring the ability for a human to draw it). Yes probably.
Leaving the design as it is currently (recurve, compound etc.) I suspect we'd use modern composites such as carbon fibre for extension (the front of the bow, carbon fibre has excellent tensile strength) and some sort of ceramic (or glass), or perhaps titanium for compression (the back of the bow).
What effect would such an arrow have down range? Well it would deliver the same energy as the bullet, so a comparable effect. 523
Though arrows do suffer from much higher wind resistance.
How far would it travel, well that depends on the weight of the arrow. I suspect it would have to be heavier than a normal arrow to cope with the stress it'd have to be made of stronger stuff. Lets go with 400g (just shy of a pound)
If we give an arrow weighing 400g a kinteic energy of 15000 joules (high calibre rifle energy) it will leave the bow at ~300m/s! So we would make an arrow weighing about a pound travel at speeds comparable to a pretty powerful hand gun bullet.
How far would it go at 45 degrees at that velocity? Well it's hard to be precise because of wind resistance, but shooting it at 45 degrees it might go between 5Km and 10Km.
Bear in mind that English Longbowmen were piercing the finest plat armour ever made at a distance of around 200m (somewhere near the end of a longbow arrow's range).
We could reasonably expect such an arrow to pass clean through a car engine.. Or stop a truck.. Just as the Barret 50 cal can.
Enjoyed all that.. hope it helps. 160