My young willow tree broke off completely at the base. Will it shoot roots again if I just place the whole tree in water/soil? Thanks
Your willow tree will root again if it's not too water-stressed.
What you should do is
dig or ask someone to dig a deep hole in the ground, to be able to put at least a quarter of the size of the whole trunk.
anchor your tree to the ground! You may use a strong stick, deeply stuck in the ground - 45° angle with the trunk, aligned in the prominent wind stream of your place
remove unnecessary branches and leaves; prune heavily to avoid too much water to evaporate - anyway, the branches and leaves that are "extra" will die soon.
Oh, yeah, it'll grow back. I'm on my second planted willow. The issue I was having, and it might be similar to yours is that it was a 6'+ tree, but it had been staked. When a plant isn't allowed to sway with the wind, crack the bark, and callous over, it's super weak. My first one was okay till the first snow storm bent it to the ground. I cut dug it up and planted a new one, which I staked with enough play to sway and build a good trunk. It took 3 years before I was comfortable removing it completely. I took the old tree, cut the trunk off about 6" from the root ball and just jammed it and the red clay stuck to the root ball, into the pot the new one came out of. Then I just set it in the puddle created by the AC and left it there all summer. It produced a skinny, but almost 6' tall shoot out of just that. I ended up planting it down at the river. So you can definitely regrow it from the stump.
Don't let the top go to waste though. Cut the rest of it up and stick it in moist soil. Just put a bunch of them in a pot of miracle grow and set the pot in a drip tray. Keep the drip tray full and let it soak up the water. You'll end up with a ton of weeping willows.
The have a natural chemical in them that promotes root growth. You can also roughly cut up what's left and stick it in a container of water and leave it out in the heat for a few weeks and the resulting water will act like a liquid root hormone for other cuttings you make.