You could do this a lot of ways... the easiest way would be to use physics plugin for your arrows and it will handle this by itself. You would just have to set the parameters for things like gravity etc, until you are satisfied with the behaviour.
You could also do this using the QARP expression. There are a few examples of using QARP floating around, but you can also read the manual entries about QARP as well. I would link you, but I'm at work and not supposed to be forum posting right now, lol!