koobas.hobune.stream
Calculate initial velocity for projectile to reach point at a given angle and calculate angle to reach point at a given velocity.
So I would like to have a turret that launches projectile in an arc at the player. To do this I need to calculate the velocity and angle at which to launch the projectile in order to hit the player. The method I have attempted so far involves first calculating the velocity needed to reach a given point at a given angle. To do this I solved for v in the equation, Δy = (Sinθ·v)(Δx/Cosθ·v) + (0.5·g)(Δx/Cosθ·v)^2 My solution was the following equation. 
x and y are respectively the horizontal and vertical distances between the turret and the target and G is equal to gravity. I used this equation to calculate the initial velocity needed to fire a projectile to the the edge of the turret's range when launched at a 45 degree angle. The following is the code used.
//_launchAngle = 45 degrees
_initialVelocity = Mathf.Sqrt((0.5f * -Physics2D.gravity.y * Mathf.Pow(_range, 2)) / (Mathf.Pow(Mathf.Cos(_launchAngle * Mathf.Deg2Rad), 2) * (0 - Mathf.Tan(_launchAngle * Mathf.Deg2Rad))));
After the initial velocity is calculated I use it in the following equation to calculate the angle to launch a projectile at in order to hit a given point(The player/target location). 
v is the initial velocity calculated at the beginning, g is gravity, and x & y are once again the horizontal and vertical distances to the target.
The issue is that the second equation always come out as NaN. From my research I am fairly confident that the equation is the correct one to use in this scenario. I have have attempted setting the points to their absolute values, and using negative gravity, however neither changed the results. I have tried different equations for velocity and they did not seem to work either. I assume I am doing something wrong, or am missing something, but I am at a loss for what that could be.
Could you share the c# code of the second formula? I have a feeling that there is a division by zero and given that the only division is by g(x) I suspect that the function of g(x) returns 0 at some point. You could help pinpoint it by assigning different variables to parts of the formula and then calculate the formula using the variables. This also makes the formula more readable. Then attach visual studio to the Unity debugger and add a breakpoint to the line with the formula. Now you can inspect the individual variables before calculating the formula.
