Shooter Aiming with Tables

[Ether]

Originally Posted by Turing'sEgo

You are given one variable, distance, and want to find 2 output variables, power (wheel speed) and angle.

No. You are given two values: the horizontal distance to, and vertical height of, the apex relative to the launch point.

From that information, you can directly compute the parabolic (no air drag) launch angle and speed.

It's all explained here.

For coordinate system XY whose origin is at the launch point,
the equation for the parabola is:

y = a*x^2 + b*x

Let the (known) apex coordinates in XY be [xp,yp]

then

a = -yp/xp^2
b = 2*yp/xp

So now you know the equation of the parabolic trajectory,
and from that you can find the launch angle theta and launch speed V:

theta = atan(b);
V = sqrt((g/2)/a)/cos(theta);

It's good to be interested in this stuff and to learn it, but for the immediate task at hand it may not be so useful. See my previous post explaining why.