I think the consensus so far is that downwind takeoffs and landings are not a good idea. Even in full-scale fighters, it's not a good idea to takeoff or land downwind. If the head/tailwind component were 10 knots, the difference in takeoff or landing groundspeed would be 20 knots. For a fighter that lands or rotates at about 150 knots (airspeed), the extra 20 knots translates into an extra 30% in kinetic energy. Landing or aborting a takeoff in a fighter (or any heavy airplane) is all about safely getting rid of kinetic energy. There is nothing smart about increasing your risk by 30%. I think the Citation pilot would agree with this.

For RC flyers, there is an additional consideration that hasn't been talked about much. I think most people takeoff and then set a climb gradient (flight path angle). If you have a big tailwind and you try to establish the same climb gradient that you would normally set with no wind, you could get yourself into big trouble. To use the numbers from the original example, suppose your takeoff speed was 15 mph and your no-wind target climb gradient is 5 degrees (pretty typical). In order to establish the same climb gradient with 10 knots of tailwind, your EFFECTIVE climb gradient would be more than 8 degrees. This effect is exaggerated if you normally set a steeper climb gradient. The bottom line is that with a tailwind, you could find yourself trying to set an effective climb gradient that is beyond the capability of your aircraft. If you don't have the common sense to take off into the wind, you need to at least be wiling to accept a shallower climb out.