Hello, I am attempting to derive an equation for some pretty specific needs. The equation I need is one that solves for the angle needed to launch a projectile at a given velocity to an object at a given distance and height different from launcher. The catch is that I would like to include the acceleration due to air resistance (which I can find later and input) as an acceleration in the x direction.
The goal is to solve for theta (I will use an o)
The only variables that can be present in the equation are:
ax, ay (gravity), x, y, v (velocity launched at, actually, it is the speed, I don't know the angle)
The equations I have been attempting to use are:
y = vy*t + (g/2)*t^2
x = vx*t + (a/2)*t^2
v = sqrt(vx^2 + vy^2)
sin o = vy/v
cos o = vx/v
The Attempt at a Solution
I keep trying to derive but keep ending up circling (deriving until I accidentally reach a variable I tried to get rid of earlier). Does anyone have an equation already derived they could show me that they could also explain how they derived, or know how I could go about deriving my goal equation successfully? Or any other formulae I should be using?