How far the paper plane can fly?

Author Credit: 
Marcin Kostur

You hold a paper plane on some height and throw it with initial speed $v_0$ at angle $\theta_0$. How far will it fly?
If you think that stronger you push further the paper plane goes? Wrong ;-), try?
 The paper plane is assumed to follow the  phugoid model with drag $R$ ;-)



This is really really cool :)