How can I find out what the name is of the tree in my garden? It is a tall tree that grows very fast. It bends over. The leaves are long, thin, and a little droopy.
That is a willow. That has a really good chance of rooting in water as it makes its own rooting hormone.
I really don't know for sure without seeing a picture but from your description sounds like a weeping willow.... What color is the bark?