I must admit that I wasn't aware of this and I'm guessing that if this is news for me it might be news for other people so I wanted to blog about it.
Turns out that the af:inputDate components in ADF Faces can actually allow your customers to select a time(hour/minutes/seconds) as well as a date.
All you have to do to see it in action is give your ADF BC EO date field the type of Timestemp instead of Date, and possibly add a nice format mask under the UI hints like: yyyy-MM-dd HH:mm:ss
and you should get a calendar popup that looks like this:
While we are on the subject of date and time, I'll put another note here that the format mask that you use for an ADF BC date or timestemp format comes from the Java Date type.
Something like the table you can find here.