Ok, for people that want to complicate thinghs more with the air resistance (noted here r):
For plane: Sp=S0+r(a(t-t0))2 - because the air resistance varies with square of the speed (I am simplyfing here). See, the air is accelerating the plane upwards, and the friction force will add to the original speed.
For Earth S=S0+a(t-t0)
Now the relative speed of plane to Earth will be Sp-S
That means Delta S= r(a(t-to)2-a(t-t0)
When this relative speed will be constant? When it will not be variable in time. So derivative of this function with the variation of time is zero.
That means r(a(t-to)/2-a=0
So the time when speed will be terminal (constant) t=2/r+t0 - so depends only of the resistance of the plane in air (given by it's shape and position).
So, again, how is this not working in FE?