Once you've killed the first dragon and been made Thane of Whiterun then go and talk to the new house earl.

Trade items with them and give them only one arrow from the most expensive set of arrows you have. After that remove their sword and assign to them a bow.

Later, when you go to battle, they will fire many arrows of the type you just gave them from the bow you just assigned them. Then, after the battle is over, you can simply go around collecting them!