Is the plane on a treadmill?
“Frictionless chicken” is funny because of the repeated vowel sound. “Spherical cows” is an old, old joke about the utility of approximations, as we all know.
But I get annoyed when folks invoke “spherical cows” in response to any approximation at all. If you don’t make approximations and SWAGs, you won’t get anywhere at all—foolish consistency is the hobgoblin of small minds, as it were.
I’m definitely not accusing the OP of this, to be clear.
So, if I bring up how no one has mentioned how the Earth’s circumference plays into this little homework assignment then I’m a hobgoblin?
You need to add the plane’s initial altitude (2000’).
It’s no mean feat for a plane to maintain a rate of climb better than 3000 fpm.
When the alternative is hitting a mountain…
Climbing at 20 degrees is not the only option. Another alternative is to circle to gain altitude. So says the pilot of a Cessna 172 in the Rocky Mountains. I do it frequently. I also fly through passes & gaps between peaks.
^ Wow! that is some Jeep! 
I’ve not piloted a plane in a long time, but I seem to remember that simply pointing the nose at a steeper angle does necessarily increase altitude. Throttle controls altitude and attitude controls airspeed. Assuming the aircraft is trimmed for level flight of course.
It’s a much more challenging trigonometry problem to ask how many chandelles need to be completed to clear the mountain.
Got the same answer using the general idea (more or less), then I started to second guess myself because 2000 → 14000 feet in 5 minutes seemed like quite a lot and I was a bit concerned that I had done something wrong with units, and also don’t planes usually fly at twenty or thirty thousand feet?
My “does this answer make sense?” intuition was not happy with this question. Then again, I know nearly nothing about flying.
Not planes that fly at 100 mph. Of course, those planes can’t pull off 3000 fpm, either.
Obviously. You never even thought to ask if the plane was on a treadmill.
This is true. The question gets around these technicalities by simply saying the plane was flown at an angle of 20º.
But an aviator would then instantly take that to be pitch of 20 degrees.
And given we don’t know the wind , then we might assume that the airspeed number is really groundspeed, or else we can’t work it out …
But oh well, we know its meant to be simple trig and so for that purpose, the angle is the flight track angle, not pitch, and airspeed is meant to be the rate along that track, roof speed if he was a person running up a roof.
“Now assume that the plane collides with an unladen swallow…”
European or African?
I don’t knowwwAAAAAAAAaaaaaggh…
splut
I’m an aviator, I didn’t take it to be a pitch of 20º (didn’t even cross my mind.)
Airspeed can only mean airspeed. We aren’t given any wind, so assume wind is zero.
My instant take on the question was that it is a trig question not a flying question. I jumped to your last paragraph immediately because I understood the context of the question.
Were we in a mood to quibble (rare, of course, for the SDMB - but bear with me here) we could dive into such things as the difference between indicated and true airspeed. (Aircraft capable of a steady 100 mph rarely offer their pilot any direct display of the latter.)