I'm trying to find the initial velocity of a projectile based on it's range. I know how to use kinematic equations to do this when air resistance is ignored, but I'm not sure how to take into account air resistance.
- initial position $(0, h)$
- a projectile with a drag force $D(v^2)$, mass $m$
- A range $h$
- Gravitational acceleration $g$
I want to find an initial velocity:
- $(0, v_i)$
I've found a number of similar problems, but they all either treat drag force as a function of $v$ rather than $v^2$, or find the range from the initial velocity.
Either an analytical or numeric solution would work.