Performance parameters suck as range and takeoff distance.
Where do you proceed from laws of motion?
Simplified Range means its probably the breguet range equation you want.
For takeoff its more complicated as there are different phases and conditional arguments required.
To get an idea you can determine the required velocity required for takeoff by knowing (or estimating) the maximum lift coefficient of the wing in its takeoff configuration and use:
lift = Lift coefficient * 0.5 * density * velocity^2 * Wing reference area
then its as simple as using S=ut+1/2at^2 (distance traveled by an accelerating body) to determine how far it has to go to get to that speed.
If you want to start being able to estimate things with any more accuracy then some light reading needs to take place. The Stamford course notes are good but quite heavy and there are great resources from NASA.