Page "Archery" Paragraph 10

When a projectile is thrown by hand, the speed of the projectile is determined by the kinetic energy imparted by the thrower's muscles performing work.

However, the energy must be imparted over a limited distance ( determined by arm length ) and therefore ( because the projectile is accelerating ) over a limited time, so the limiting factor is not work but rather power, which determined how much energy can be added in the limited time available.

Power generated by muscles, however, is limited by force – velocity relationship, and even at the optimal contraction speed for power production, total work done by the muscle will be less than half of what could be done if the muscle were contracting over the same distance at very slow speeds, resulting in less than 1 / 4 the projectile launch velocity possible without the limitations of the force – velocity relationship.