If a rocket launches from Florida, how far around the world does it travel before it reaches orbit? Is it in space before it completes crossing the Atlantic?
Does it vary for different powered rockets, or is it typically the same trajectory?
It varies with different rockets, but typically insertion to low Earth orbit is achieved around 1200-1500 miles (~2000-2500 km) downrange distance — something less than halfway across the Atlantic for an Eastward launch from Cape Canaveral.
The longer the ascent, the further downrange it will be before orbital insertion.
Here's one example for a 10-minute ascent (note that the horizontal axis is linear in downrange distance, not in time):
Note that the rocket will be in space long before this point; the 100km Kármán line is reached at less than 100km downrange distance in the trajectory shown.