"Perfect Physics"

I have recently been working with more Physics simulations in Blender. I’m not very skilled with them, however, I was wondering if there was a way that I could make a sort of ‘perfect physics’. Something where I could (perhaps) set the end keyframe and beginning keyframes, and then have it do the rest of the work. In my example, I launch an arrow at the box, and I’m trying to see if there is any way to get it perfectly in the center. On a side note, is there any way that I can have the arrow stick in the bag? The only thing I have tried is inserting a keyframe where it sticks and having the physics stop there.

Thank you very much!

Blend file:
arrowbag.blend (850 KB)