I'm trying to solve projectile motion using 2D Runge-Kutta method. The friction coefficient (in units of mass) is given by
$$ B_2/m= C + \frac{D}{1+\exp[ \frac{v^* - v_d}{\Delta}]} $$
where $D=0.0039$, $C=0.0058$, $v_d=35 m/s$ and $v^*$ is the velocity of the projectile respect to the air frame
I understand that the equations of motion that I have to solve are
$$\frac{dv_x}{dt}= - \frac{B_2}{m} \sqrt{v_x^2+v_y^2} \cdot v_x \quad \quad \frac{dx}{dt}=v_x $$ $$\frac{dv_y}{dt}= - g - \frac{B_2}{m} \sqrt{v_x^2+v_y^2} \cdot v_y \quad \quad \frac{dy}{dt}=v_y. $$
The problem is that I'm not sure about the relation between $(v_x, v_y)$ and the components of $v^*$, because I don't have the velocity of the air in the Earth frame to compute the velocity of the projectile in the Earth frame and make a relation between it and the air frame
