How do you get past the door that needs a key in the arrow of extrication quest in oblivion

You need to shoot the arrow into a central pillar that rises up after you press two buttons on opposite ends of the room. It helps to be invisible the whole time so you don't have to fight the high-level monsters in the room with you.

The shot takes practice, since you need to take it from pretty far away. If you don't hit the exact right spot, the door won't open. If you do miss, you have to retrieve the arrow.