A siege is to cut off all supplies and wait for the enemy to give up. Sometimes a siege would take months of waiting before the enemy would surrender. A siege was used to lesson the struggle and deaths that a battle brings.
The ballista is a medieval crossbow. Ballista's were typically made of wood. They shot large bolts that could weigh up to 10 pounds! The first ballista was created in 400 b.c. It was created to fire long range and be more accurate that a trebuchet. The way the ballista works is there