Adding some shot utilities. Needs review

src/main/java/frc/robot/utilities/Utilities.java

@@ -10,6 +10,8 @@ public class Utilities {
 
     static Boolean Red = false;
 
+    public static final double kG = -9.81;
+    
     public static Alliance ShiftFirst() {
         gameData = DriverStation.getGameSpecificMessage();
 
@@ -27,4 +29,52 @@ public class Utilities {
         return null;
     }
 
+    /**
+     * A ChatGPT possible hallucination related to calcuating whether a shot is possible
+     * for a given speed and change in X and Y position
+     * 
+     * Note that X in this scenario is the physical distance from the shooter exit to 
+     * target. Y is the change in height from the shooter exit to the target height
+     * 
+     * TODO Review ChatGPT's math more thoroughly, preferably with someone with fresher math skills
+     * 
+     * @param targetVMPS The target velocity of the shooter in Meters per Second
+     * @param deltaXM The "as the crow flies" distance between the shooter exit and the target
+     * @param deltaYM The height difference between the shooter exit and the target
+     * @return A true or false value indicating whether the shot is possible
+     */
+    public static boolean shotPossible(double targetVMPS, double deltaXM, double deltaYM) {
+        return Math.pow(targetVMPS, 4) >= 
+            -9.81 * (-9.81 * Math.pow(deltaXM, 2) + 2 * deltaYM * Math.pow(targetVMPS, 2));
+    }
+
+    /**
+     * A ChatGPT possible hallucination that calculates the angle required to make a shot for
+     * a given speed and change in X and Y position
+     * 
+     * Note that X in this scenario is the physical disatance from the shooter exit to
+     * target. Y is the change in height from the shooter exit to the target height
+     * 
+     * Setting softerShot to true changes the angle of attack to a soft, long range shot. False
+     * makes the shot more of a lob
+     * 
+     * TODO Review ChatGPT's math more thoroughly, preferably with someone with fresher math skills
+     * 
+     * @param targetVMPS The target velocity of the shooter in Meters per Second
+     * @param deltaXM The "as the crow flies" distance between the shooter exit and the target
+     * @param deltaYM The height difference between the shooter exit and the target
+     * @param softerShot True for a long range shot, false for a short range lob
+     * @return The angle required of the shooter to make the shot described by the input parameters
+     */
+    public static double shotAngle(double targetVMPS, double deltaXM, double deltaYM, boolean softerShot) {
+        double vPow2 = Math.pow(targetVMPS, 2);
+        double vPow4 = Math.pow(targetVMPS, 4);
+        double sqrtPiece = Math.sqrt(vPow4 - kG * (kG * Math.pow(deltaXM, 2) + 2 * deltaYM * vPow2));
+
+        if(softerShot) {
+            return Math.atan((vPow2 - sqrtPiece) / (kG * deltaXM));
+        } else {
+            return Math.atan((vPow2 + sqrtPiece) / (kG * deltaXM));
+        }
+    }
 }