Avi8tor - reading between the lines of your Cub example, your point seems to be "don't confuse me with energies, forces or momentum; we all know a Cub hasn't got the horsepower to accelerate that quickly, so it MUST drop out of the sky".
I believe that the answer to your confusion is that, in the ground-based frame of reference that you are considering, the "horsepower" is in the 60 knot wind that's blowing! Remember, your little Cub is blatting away as hard as it can, indicating 60 knots airspeed into wind, even though it is stationary. Pretty much any manouever that stops it pointing into wind will immediately "accelerate" the airframe down-wind, at least from the point of view of a ground based observer. For example, if you close the throttle and pull the nose straight up to the vertical, the subsequent stall and tail-slide will appear - to the ground observer - to be travelling down-wind at the aforementioned 60 knots. For our hapless aerobatic pilot it's going to look pretty bizarre out of the window, and she's probably going to crash, but that's where we came in on downwind turns.
So, back to your example, as the Cub pilot starts the 180 degree downwind turn, they progressively stop fighting the wind. As they turn away from the wind, the wind itself contributes the 60 knot component so that, yes, when we are 90 degrees around the turn we will be going sideways at 60 knots over the ground (but perfectly balanced in the air).
This explanation certainly works for me. In fact, now I'm just waiting for a strong steady wind so that I can practice flying backwards
