Прыжок считается точно: высота подбирается обратным счетом

Формула v = 0.42 * sqrt(h / 1.25) давала 1.48 вместо 1.5, потому что движение
каждый тик теряет часть на сопротивление воздуха. Теперь высота находится
обратным счетом по физике ваниллы (гравитация 0.08, сопротивление 0.98).

Высота -> импульс: 1.25 -> 0.41961, 1.35 -> 0.43713, 1.5 -> 0.46341,
1.6 -> 0.48093, 2.0 -> 0.54485.

Задаётся: run-game.ps1 -ExtraArgs "-Drsx.jumpHeight=1.5"

game-fork/src-overlay/net/rustnotmc/client/RsxPlayerTuning.java

@@ -42,6 +42,12 @@ public final class RsxPlayerTuning {
     /** The speed the vanilla jumps with. */
     private static final float VANILLA_JUMP_MOTION = 0.42F;
 
+    /** How fast the motion falls on every tick. */
+    private static final float GRAVITY = 0.08F;
+
+    /** How much of the motion the air takes on every tick. */
+    private static final float AIR_DRAG = 0.98F;
+
     private RsxPlayerTuning() {
     }
 
@@ -78,15 +84,43 @@ public final class RsxPlayerTuning {
     /**
      * The upward speed a jump of that height needs.
      *
-     * The vanilla jumps with 0.42 and that carries it 1.25 blocks. The height
+     * The height of a jump is not the square of the speed, because the
-     * grows with the square of the speed, so the speed for a height is the
+     * motion loses a little to the air on every tick. So the speed is found
-     * vanilla one times the square root of the ratio.
+     * the honest way: the height is computed for a guess and the guess is
+     * corrected until it is the height that was asked for.
      */
     public static float jumpMotion(float height) {
         if (height <= 0.0F) {
             return VANILLA_JUMP_MOTION;
         }
-        return VANILLA_JUMP_MOTION * (float) Math.sqrt(height / VANILLA_JUMP_HEIGHT);
+        float low = 0.0F;
+        float high = 1.0F;
+        for (int i = 0; i < 60; i++) {
+            float middle = (low + high) * 0.5F;
+            if (heightOf(middle) < height) {
+                low = middle;
+            } else {
+                high = middle;
+            }
+        }
+        return (low + high) * 0.5F;
+    }
+
+    /**
+     * How high a jump with that speed carries the player.
+     *
+     * The motion of the vanilla on every tick: the speed falls by the
+     * gravity and then by the air. The player is as high as the sum of the
+     * upward steps.
+     */
+    private static float heightOf(float motion) {
+        float height = 0.0F;
+        float speed = motion;
+        while (speed > 0.0F) {
+            height += speed;
+            speed = (speed - GRAVITY) * AIR_DRAG;
+        }
+        return height;
     }
 
     private static float setting(String name, float fallback, float floor) {