My ultimate goal is to find the angle of elevation necessary to launch a projectile from the origin to (x,y) with initial velocity V and under gravitational acceleration g. Wind resistance is ignored.
This is where I've started, and the path I've taken. First, I took the parametrics for x and y.
x = V * cosθ * t
y = V * sinθ * t - (g / 2) * t^2
-Then, I found t in terms of x, V and θ...
t = x / (V * cosθ)
-I plugged that value in for t in the y equation...
y = V * sinθ* (x / (V * cosθ)) - (g / 2) * (x^2 / (V^2 * (cosθ)))
y = x * tanθ - (g * x^2) / (2 * V^2 * (cosθ)^2)
I don't know what to do from here. I need to find θ in terms of x, y, V, and g, but it seems impossible to get all of the θ's into a single term. (x, y, V and g will be known when I use the equation).