One of the many activities you can participate in the SCA is Archery. There are two different classes: Combat Archery and Target Archery.
Combat archery is used in conjunction with field combat in battle situations. This requires restrictions on power or poundage of the recurve bow, and arrows of a safe design to hit men in armor. Trebuchets, ballistas, and catapults are included in this class as siege weapons. Here are pictures of ballistas.
Target archery and Thrown Weapons are used for populace battle points in many of the "wars", as well as for fun by the participants. Archery shoots can be as simple as lining up and shooting at a target with the highest score being the winner, to various novelty shoots. A very short list of novelties includes storming the castle, defending the castle, tower shoots, War of the Roses, duck-goose!, friend-foe, berserker, York, modified York. The archery link below can bring you to links with these and other shoots listed in greater detail.
If you prefer to throw your weapons, you can find various weapon styles where particiants throw common medieval weapons such as axes, knives, and spears at solid wood targets.
Unlike the combat archers, these activities are open to all without needing special training and authorizations. There frequently are loaner bows, arrows, knives, axes etc. for the populace to borrow and join in the fun. You just need to listen to the marshals! (As in all martial activities, marshals are present to inspect equipment, run the range, and ensure that everyone participates safely.)
As seen here, a shoot can be very serious indeed for the participants:
For more, go to http://www.sca.org/resources/martial-activities/archery-tw/.
These are pictures from the White Stag competition held by the Company of the Ironwolf. Sir Osric Eisenwulf, Knight of the SCA and head of the Company of the Ironwolf is in the first picture on the right side of the picture giving instruction to the archers on the rules of the tournament. Bryn Archer is in white (having just fired her shot) in the second picture with the ultimate winner of the competition in the foreground - Taurus (ready to release his shot), and The Honorable Lady Saehilder is in the third picture (ready to fire). The last picture id fron It Takes My Child to RAZE A Village showing all ages can participate in Archery.