The origin of bows and arrows is not really known, but it is a fact that they were used widely in hunting and warfare in every continent for centuries past.
The Anglo-Saxons first developed short bows that were about three feet long, but never really became a major fighting weapon, because of their limited range, and inability to pierce any form of armour. They were, however, effective against unarmoured people. Archery was more in use and quite effective in hunting, as it could bring down prey situated even hundreds of feet away.
The advent of crossbows led to archery that was more effective in battle. In traditional short bows, the draw is maintained manually, until the bowstring is released to launch the arrow. In a crossbow, the drawstring is locked through a mechanism, and the arrow launched by releasing this lock. This greatly increased the distance to which arrows could be shot, and also the power of the arrow itself. This did reduce the firing rate, but its effectiveness led to crossbows being used by Saxons during the war after the battle of Hastings in 1066. As a matter of fact, they were considered such lethal weapons, that Christians were excommunicated if they used it against fellow Christians. Large groups of crossbowmen became an integral part of armies of that period. Even forts were redesigned to provide special slits that allowed the discharge of these crossbows.
Longbows that were about 6 feet in length were always in use along with short bows and crossbows, and often made an effective weapon of war, when used by trained and accurate archers, and even proved very lethal against cavalry. A combination of longbows and crossbows made for very effective weapons in the waging of war during the medieval days, until they were taken over by the advent of muskets.