Need formula to calculate Max Distance and Required Force

Hi,

I'm working on a Top Down 2D game which uses physics to propel and bounce objects around the scene. However, I admit I'm no math wiz, so I was hoping someone might be able to help me out with a few formulas.

1 - Get the Distance an object can travel given a specified amount of Force.

2 - Get the Force required to travel a certain Distance.

Here are (what I assume to be) the primary components/properties to consider:

Angular friction/drag/rotation is always ignored.
Rigidbody's Linear Drag is always 0. Instead, we use the FrictionJoint2D.

The Rigidbody's Mass varies but it is usually 0.25, 1, or 2
FrictionJoint2D's Max Force varies, but is usually 7, 25, or 50

rigidbody.AddForce() is always used to get the objects moving, with the ForceMode2D.Impulse type.

Below is an example of the gameplay. These formulas will assist the AI in making decent shots of it's own!

Would love to talk more with a Physics wiz! Thank you!

 

Figured it out and posting the results incase anyone else ever needs this kind of thing

Code (CSharp):

1. public void AddForce()
2.     {
3.         _rb.AddForce(Force * Direction, ForceMode2D.Impulse);
4.        
5.         var friction = _frictionJoint.maxForce;
6.         var predictionDistance = Math.Pow(Force, 2) / (2 * friction * _rb.mass);
7.        
8.         var requiredForce = Math.Sqrt(predictionDistance * 2 * friction * _rb.mass);
9.        
10.         Debug.Log($"Force: {Force}, Friction: {friction}, Distance Predicted: {predictionDistance} ");
11.         Debug.Log($"Required Force: {requiredForce}");
12.     }