feat(gs/xanthous): Allow throwing rocks

Implement a first pass at a "fire" command, which allows throwing rocks,
the max distance and the damage of which is based on the weight of the
item and the strength of the player.

Currently the actual numbers here likely need some tweaking, as the
rocks are easily throwable at good distances but don't really deal any
damage.

Change-Id: Ic6ad0599444af44d8438b834237a1997b67f220f
Reviewed-on: https://cl.tvl.fyi/c/depot/+/3764
Reviewed-by: grfn <grfn@gws.fyi>
Tested-by: BuildkiteCI

users/grfn/xanthous/src/Xanthous/Physics.hs

@@ -0,0 +1,71 @@
+--------------------------------------------------------------------------------
+module Xanthous.Physics
+  ( throwDistance
+  , bluntThrowDamage
+  ) where
+--------------------------------------------------------------------------------
+import Xanthous.Prelude
+import Xanthous.Data
+       ( Meters
+       , (:**:)(..)
+       , Square
+       , Grams
+       , (|*|)
+       , (|/|)
+       , Hitpoints
+       , Per (..)
+       , squared
+       , Uno(..), (|+|)
+       )
+--------------------------------------------------------------------------------
+
+-- university shotputter can put a 16 lb shot about 14 meters
+-- ≈ 7.25 kg 14 meters
+-- 14m = x / (7.25kg × y + z)²
+-- 14m = x / (7250g × y + z)²
+--
+-- we don't want to scale down too much:
+--
+-- 10 kg 10 meters
+-- = 10000 g 10 meters
+--
+-- 15 kg w meters
+-- = 15000 g w meters
+--
+-- 14m = x / (7250g × y + z)²
+-- 10m = x / (10000g × y + z)²
+-- wm = x / (15000g × y + z)²
+--
+-- w≈0.527301 ∧ y≈0.000212178 sqrt(x) ∧ z≈1.80555 sqrt(x) ∧ 22824.1 sqrt(x)!=0
+--
+-- x = 101500
+-- y = 0.0675979
+-- z = 575.231
+--
+
+-- TODO make this dynamic
+strength :: Meters :**: Square Grams
+strength = Times 10150000
+
+yCoeff :: Uno Double
+yCoeff = Uno 0.0675979
+
+zCoeff :: Uno Double
+zCoeff = Uno 575.231
+
+-- | Calculate the maximum distance an object with the given weight can be
+-- thrown
+throwDistance
+  :: Grams  -- ^ Weight of the object
+  -> Meters -- ^ Max distance thrown
+throwDistance weight = strength |/| squared (weight |*| yCoeff |+| zCoeff)
+
+-- | Returns the damage dealt by a blunt object with the given weight when
+-- thrown
+bluntThrowDamage
+  :: Grams
+  -> Hitpoints
+bluntThrowDamage weight = throwDamageRatio |*| weight
+  where
+    throwDamageRatio :: Hitpoints `Per` Grams
+    throwDamageRatio = Rate $ 1 / 5000