Catapults as siege weapons became ineffective in 885-886 AD rendered useless by new defense technology, but they still continues to be used in military operations. The last large scale use of catapults as a weapon delivery device was in World War 1. Catapults were used to throw hand grenades across No Man's Land and into enemy trenches. Unfortunately for catapults they were soon replace with small mortars.
Now catapults are used in target practice to shoot clay pigeons in the air, to launch food at siblings, and the most common use to launch planes into the air.
An aircraft carrier doesn't have the runway space to allow for a plane to accelerate to take off as it would on the ground so an catapult is used to propel the aircraft into the air in a very short distance.
To see a aircraft carrier catapult in action check out : http://www.getamused.com/videos/Aircraft_Carrier_Catapult.html
This image is courtesy of : http://www.fas.org/programs/ssp/man/uswpns/navy/aircraftcarriers/carriers.html
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