Setting up an inverse kinematic rig with multiple segments.

I am trying to make a bending springboard for a game. I would like the player to be able to click on the tip of the board, pull it down and release it to launch an object into the air at differing angles. So far I have tried a few different ways of getting this to work. I can't simply use a preset animation because that does not allow the player to change the angle of the launched object. I have tried playing around with hinge joints on the models armature a lot, but unfortunately that doesn't seem to give me the effect I am looking for.

I think what I need is to setup inverse kinematics for my models armature in Unity. Unfortunately, everything I research for IKs in Unity just talks about how to set up humanoid limbs. Or it points to the Unity Asset Store IK script for humanoid arms. This will not work very well for my needs as my model will need several more points of articulation to give it a good bending effect. I know that this is possible since IK obviously works for arms and I have found a YouTube video of someone showing off the effect that I am looking for in Unity (which I will post below), but I just don't know how to set something like this up for an object with several more joints.

Here is an example of the effect I am looking for.

Thanks in advance for any help!