I've been involved in two go arounds. Both with BA. The first was on an Airbus coming into Glasgow and the second on a 737 into Gatwick. I have to say that the Airbus blasted off like a rocket.
In both cases there was concern in the cabin. Not least from me. My head was telling me that things were under control, but logic does not necessarily win when a smooth approach to landing (both occasions took place on lovely sunny days) are transformed into climbs at a rate I had not experienced before.
In both cases the crew handled matters very, very well. Within a minute of the plane levelling, there was a very short announcement. In both cases a previous plane had been slow to clear the runway. I may have been fortunate, but my experience is that these matters are handled very well by crews.