Arrow
The bow and arrow originates from the Atlatl, (en.wikipedia.org/wiki/Atlatl) the first mechanical projectile weapon.
The mass of the arrow does not affect the kinetic enery of the projectile. It does however affect the velocity of the arrow. The heavier the arrow the slower it flies ( out of the same bow). As far as penertation goes, velocity is your friend. There is alot of material science that goes into play but generally the faster projectile wins in penetration tests.
to Bullet.
Gravity pulls everything on earth down which gives an arrow that shoots horizontilly its vertical movements.
An object that is used for killing animals, indians made them out of wood.
The magnitude of its Velocity (Speed), and its Direction. These are the components of the Arrow (Vector) that represents its MOTION.
You cannot get specific odds from such a broad question. The arrow's/bolt's thickness, the shot consistency of the archer, the raw power of the bow and the projectile's genera quality will help make splitting an arrow more likely.
What you really need to find out is how fast the projectile will leave the arrow. The projectile's MASS (not its weight) and the force with which the bow pushes it can help you calculate the acceleration (using Newton's Second Law), but that's really insufficient information - you also need to know for how long the bow pushes the projectile, using the given force.
if you are asking with a gun or arrow that's a yes the projectile is moving so quickly it will cut the hair in half
The protection enchantment will take a certain percentage of any form of damage dealt to you and put the damage on your armour not the player. Projectile projection does the she thing but only when you are hit by projectiles (e.g. an arrow)
A projectile is an object moving through the air but people mainly think of a projectile as something you aim at someone and attempt to hit them with. A rock, a bullet, an arrow, a missle, all can be considered projectiles. The first sentence of the answer though is what you are looking for I think.