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The the new movie, The Hobbit: The Desolation of Smaug, a short segment in the film mention Bard the Bowman's ancestor, Girion failed to kill the dragon, Smaug with the Black Arows, but how? well for starters, Girion failed to properly allign the longbow to a good 45 degree angle so he can launch the projectile accuratly. also he needed to apply more force on the black arrows so that newton's third law may apply so that the amount of force Girion put into the arrows would have an equal amount once piercing the dragon's hide, preventing it from destroying the city of Dale. However, Bard will rectify this mistake by providing more work into the last black arrow with the speed of his hast to get the arrow onto the bow and having the proper potential energy needed to fire the arrow at smaug's weak spot.
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