Let's say I have a projectile being thrown by a player in my 2-D game. I want to work backwards and find the initial velocity to apply to the projectile such that it passes through a target point in space given that the launch point might not be at $y=0$.
Some applications of this would be a basketball shot simulator or a pub darts simulation.
- initial or launch angle: $\theta_o$
- initial or launch height: $y_o$
- target point: ($x_f$, $y_f$)
- constant acceleration due to gravity ($g$)
- air resistance ignored
I need to find:
- initial launch velocity: $v_o$
Here's an image of what I'm talking about.
I am interested in learning the derivation of the answer not just a formula that I plug-and-chug. Thanks!