They exist today. There are air guns used in small and big game hunting.

This company sells air rifle that can fire a .45 cal projectile from 900fps to 1500fps. Check Air Gun Depot.

For example this gun actually is a double barrel .50 cal air gun that shoots each projectile out at 1130fps.

And this was just a quick web search for air guns that are capable of hunting large game. I would probably bet you could find airguns set the fire such a deadly projectiles such as 30 cal outwards of 2000fps.

They exist today. There are air guns used in small and big game hunting.

This company sells air rifle that can fire a .45 cal projectile from 900fps to 1500fps. Check Air Gun Depot.

For example this gun actually is a double barrel .50 cal air gun that shoots each projectile out at 1130fps.

Seneca Double Shot .50 cal Air Gun

And this was just a quick web search for air guns that are capable of hunting large game. I would probably bet you could find airguns set the fire such a deadly projectiles such as 30 cal outwards of 2000fps.

EDIT: below is an image of the US Air Force is air gun that can shoot a 30 caliber projectile from 1000fps to 1300fps, depending on whether you get the long barrel or the carbine. Pictured below is the long barrel version which is also available in 45 caliber and it shoots that at 930fps.

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Here is part of the description of this rifle:

The US AirForce Texan made headlines throughout the firearm industry when upon release it was billed the world's most powerful production air rifle. The Texan turned heads then, and AirForce building upon that success with the AirForce Texan SS big bore air rifle!