I need to calculate the angle required to launch a projectile from point A to point B on an uneven ground, given the parameters. 0nly gravity acts on the projectile – no air resistance.
Parameters given:
$d$ : range or distance
$v_{i}$ : initial velocity
$g$ : gravity
$y_{0}$ : launch height
Parameter to calculate:
$\theta$ : launch angle
I have found this formula to get distance travelled by the projectile
$d=\frac{ v_{i}cos\theta }{ g }( v_{i}sin\theta + \sqrt{ (v_{i}sin\theta)^{2}+2gy_{0} })$
From the above formula, I rearranged variables to get the initial velocity for a given angle. Like this:
$v_{i}^{2}=\frac{d^{2}g}{2(cos\theta)^{2}(y_{0}+d*tan\theta)}$
In the same way, I was trying to get that formula in terms of the angle. Like
$\theta=...$
But the far I got was
$y_{0}(cos\theta)^{2}+d*sin\theta*cos\theta=\frac{d^{2}g}{2v_{i}^{2}}$
From that point on, I could not resolve the equation.
I am looking for a formula to set the 4 parameters above and get the angle (or if it exists or not, or if the projectile will reach point B with the initial velocity or not) to launch the projectile. I would like to know if what I am triying to do is possible or projectile motion doesnt work this way.
I also found this one, to calculate the maximum range for angle.
$\theta=arccos(\sqrt{\frac{2gy_{0}+v^{2}}{2gy_{0}+2v^{2}}})$
It is almost what I am looking for but it doesnt take into account the distance.
