Should have been more careful with my example.
The point I was trying to make is that while at 60 miles up you don't end up going very fast before atmosphere starts slowing you, you can build up a huge velocity by falling straight toward the Earth in a vacuum from miuch further out in space. If you go out far enough from Earth, and magically stop somehow relative to the Earth (it will continue to revolve under you), this end velocity becomes pretty much equal to Earth's escape velocity, about 25,000 mph.
I don't know what this vertical distance would actually be--"g" varies as you go outward, and the calculation now becomes what I call work. Almost certainly it's more than a thousand miles.