Slings were in use long before David and Goliath. With little physical strength, objects could be hurled at great speed and distance. So, given the required accuracy, David could have killed Goliath.
However, this biblical story has another twist. It wasn't included in the Book of Chronicles. This may imply that it was added to 1 Samuel after the Babylonian Exile, centuries after David fought Goliath. Therefore, it may be a myth!