The problem I am trying to solve is to find the velocity needed to hit an elevated target a known distance away from the initial position of a launcher.
We know the height of and distance to the elevated target. We also know the initial launch angle of the projectile. We do not know how long it will take for the projectile to reach the target. We are trying to solve for the initial velocity.
I have scoured the internet (including this stackexchange) for a solution, but all of the solutions I have come across seem to only work when the target is at the same elevation as the launcher (which would not work in my situation).
I have also tried to derive my own equation for the initial velocity. I got pretty close, but it is in a form where I cannot isolate the initial velocity in the equation.
d is the distance to the target
h is the height of the target
theta is the launch angle
vi is the initial velocity
To clarify, I derived this equation using conservation of energy, and plugging in other equations I derived, but there are many ways to come to this equation.