diff --git a/Packages/com.vrcbilliards.vrcbce/Runtime/Scripts/BasePoolStateManager.cs b/Packages/com.vrcbilliards.vrcbce/Runtime/Scripts/BasePoolStateManager.cs
index 9850dec..116134c 100644
--- a/Packages/com.vrcbilliards.vrcbce/Runtime/Scripts/BasePoolStateManager.cs
+++ b/Packages/com.vrcbilliards.vrcbce/Runtime/Scripts/BasePoolStateManager.cs
@@ -1850,6 +1850,9 @@ private void OnLocalTurnStart()
             {
                 ResetTimer();
             }
+
+            // sanitize old cue tip location data to prevent stale data from causing unintended effects.
+            localSpacePositionOfCueTipLastFrame = tableSurface.transform.InverseTransformPoint(cueTip.transform.position);
         }
 
         private void OnNewGameStarted()
@@ -3303,4 +3306,4 @@ private void PlayAudioClip(AudioClip clip)
             mainSrc.PlayOneShot(clip);
         }
     }
-}
\ No newline at end of file
+}
diff --git a/Packages/com.vrcbilliards.vrcbce/Runtime/Scripts/PoolStateManager.cs b/Packages/com.vrcbilliards.vrcbce/Runtime/Scripts/PoolStateManager.cs
index d7b13ac..6203f51 100644
--- a/Packages/com.vrcbilliards.vrcbce/Runtime/Scripts/PoolStateManager.cs
+++ b/Packages/com.vrcbilliards.vrcbce/Runtime/Scripts/PoolStateManager.cs
@@ -328,7 +328,7 @@ protected override void HitBallWithCue(Vector3 shotDirection, float velocity)
 
             float a = jkPlane.GetDistanceToPoint(Q);
             float b = Q.y - o.y;
-            float c = Mathf.Sqrt(Mathf.Pow(ballRadius, 2) - Mathf.Pow(a, 2) - Mathf.Pow(b, 2));
+            float c = Mathf.Sqrt(Mathf.Max(0,Mathf.Pow(ballRadius, 2) - Mathf.Pow(a, 2) - Mathf.Pow(b, 2)));
 
             float adj = Mathf.Sqrt(Mathf.Pow(q.x, 2) + Mathf.Pow(q.z, 2));
             float opp = q.y;
@@ -352,7 +352,7 @@ protected override void HitBallWithCue(Vector3 shotDirection, float velocity)
 
             // https://billiards.colostate.edu/physics_articles/Alciatore_pool_physics_article.pdf
             float alpha = -Mathf.Atan(
-               (5f / 2f * a / ballRadius * Mathf.Sqrt(1f - Mathf.Pow(a / ballRadius, 2))) /
+               (5f / 2f * a / ballRadius * Mathf.Sqrt(Mathf.Max(0,1f - Mathf.Pow(a / ballRadius, 2)))) /
                (1 + MASS_OF_BALL / m_e + 5f / 2f * (1f - Mathf.Pow(a / ballRadius, 2)))
             ) * 180 / Mathf.PI;
 
@@ -1260,4 +1260,4 @@ private void TriggerPocketBall(int id)
             ));
         }
     }
-}
\ No newline at end of file
+}