[FEAT] Add general purpose Projectile Motion algorithm (Physics) (#6928)

[FEAT] Add general purpose Projectile Motion algorithm

Co-authored-by: Priyanshu1303d <priyanshu130d@gmail.com>
Co-authored-by: Deniz Altunkapan <deniz.altunkapan@outlook.com>

src/main/java/com/thealgorithms/physics/ProjectileMotion.java

@@ -0,0 +1,96 @@
+package com.thealgorithms.physics;
+
+/**
+ *
+ * This implementation calculates the flight path of a projectile launched from any INITIAL HEIGHT.
+ * It is a more flexible version of the ground-to-ground model.
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Projectile_motion">Wikipedia - Projectile Motion</a>
+ * @author [Priyanshu Kumar Singh](https://github.com/Priyanshu1303d)
+ */
+public final class ProjectileMotion {
+
+    private ProjectileMotion() {
+    }
+
+    /** Standard Earth gravity constant*/
+    private static final double GRAVITY = 9.80665;
+
+    /**
+     * A simple container for the results of a projectile motion calculation.
+     */
+    public static final class Result {
+        private final double timeOfFlight;
+        private final double horizontalRange;
+        private final double maxHeight;
+
+        public Result(double timeOfFlight, double horizontalRange, double maxHeight) {
+            this.timeOfFlight = timeOfFlight;
+            this.horizontalRange = horizontalRange;
+            this.maxHeight = maxHeight;
+        }
+
+        /** @return The total time the projectile is in the air (seconds). */
+        public double getTimeOfFlight() {
+            return timeOfFlight;
+        }
+
+        /** @return The total horizontal distance traveled (meters). */
+        public double getHorizontalRange() {
+            return horizontalRange;
+        }
+
+        /** @return The maximum vertical height from the ground (meters). */
+        public double getMaxHeight() {
+            return maxHeight;
+        }
+    }
+
+    /**
+     * Calculates projectile trajectory using standard Earth gravity.
+     *
+     * @param initialVelocity Initial speed of the projectile (m/s).
+     * @param launchAngleDegrees Launch angle from the horizontal (degrees).
+     * @param initialHeight Starting height of the projectile (m).
+     * @return A {@link Result} object with the trajectory data.
+     */
+    public static Result calculateTrajectory(double initialVelocity, double launchAngleDegrees, double initialHeight) {
+        return calculateTrajectory(initialVelocity, launchAngleDegrees, initialHeight, GRAVITY);
+    }
+
+    /**
+     * Calculates projectile trajectory with a custom gravity value.
+     *
+     * @param initialVelocity Initial speed (m/s). Must be non-negative.
+     * @param launchAngleDegrees Launch angle (degrees).
+     * @param initialHeight Starting height (m). Must be non-negative.
+     * @param gravity Acceleration due to gravity (m/s^2). Must be positive.
+     * @return A {@link Result} object with the trajectory data.
+     */
+    public static Result calculateTrajectory(double initialVelocity, double launchAngleDegrees, double initialHeight, double gravity) {
+        if (initialVelocity < 0 || initialHeight < 0 || gravity <= 0) {
+            throw new IllegalArgumentException("Velocity, height, and gravity must be non-negative, and gravity must be positive.");
+        }
+
+        double launchAngleRadians = Math.toRadians(launchAngleDegrees);
+        double initialVerticalVelocity = initialVelocity * Math.sin(launchAngleRadians); // Initial vertical velocity
+        double initialHorizontalVelocity = initialVelocity * Math.cos(launchAngleRadians); // Initial horizontal velocity
+
+        // Correctly calculate total time of flight using the quadratic formula for vertical motion.
+        // y(t) = y0 + initialVerticalVelocity*t - 0.5*g*t^2. We solve for t when y(t) = 0.
+        double totalTimeOfFlight = (initialVerticalVelocity + Math.sqrt(initialVerticalVelocity * initialVerticalVelocity + 2 * gravity * initialHeight)) / gravity;
+
+        // Calculate max height. If launched downwards, max height is the initial height.
+        double maxHeight;
+        if (initialVerticalVelocity > 0) {
+            double heightGained = initialVerticalVelocity * initialVerticalVelocity / (2 * gravity);
+            maxHeight = initialHeight + heightGained;
+        } else {
+            maxHeight = initialHeight;
+        }
+
+        double horizontalRange = initialHorizontalVelocity * totalTimeOfFlight;
+
+        return new Result(totalTimeOfFlight, horizontalRange, maxHeight);
+    }
+}