To make matters more fun there is the wonderful subject of "screen height". This is an imaginary screen which the lowest bit i.e. the landing gear, has to clear at V2. For an all engines take off screen height is 35 feet. In the event of an engine failure you are allowed to strain and pucker to a height of 15 feet, thus lurching across the M25 safely.
There are all kinds of scams available to use available runway to increase takeoff weight and therefore stagger into the sky at the last possible moment with the max allowable payload.
if t'were not so then international aviation would hang up it's clogs.
If you have ever run into the expression "backside of the drag curve", then you have an idea of the problems facing an airliner at v2.
The fuel laden monster is dragged into the sky at the minimum airspeed by dint of flaps/slats/slots which increase lift but also increase drag.
Once you clean up the wing then the aircraft has a chance to accelerate to a speed where lift will increase with airspeed and induced drag disappears down the plug hole leaving you with excess thrust to shove you away from the awful earth beneath.