Oops - I missed the fastest possible bit and went with "pretty darn good" - round number:

American Baseball pitcher: 40 m/s, 130 fps, 90 mph
Practiced slinger: 45-50 m/s, 165 fps, 110 mph
Strong Slinger: 60 m/s, 200 fps ,130 mph
Tint: 70 m/s, 220fps, 150 mph 
Jurek and the record setters: 90m/s+, 300fps, 200 mph

60 m/s should comfortably put a rock over 200m.

200 fps, although not particularily fast by rifle or compound crossbow standards, is still pretty darned fast.

If you figure the energy of the glans moving 200fps (100g) you end up with 140 foot-pounds energy, not far off what a .50 cal black-powder pistol would have made, and almost triple the energy delivered by a modern bow. By the time you are throwing in the upper end of our range the energy is starting to push .45 ACP levels. The shock of impact is very high.

So be careful.

Matthias