Actually the momentum has nothing to do with it due to the fact that momentum is not a force. The law of conservation of energy states that energy in = energy out+ energy stored. The energy out is directly related to distance and the energy stored to heat or friction. The friction is generally ignored due to:1) the complexity of the equationsand 2) it's minimal rolein aero and fluid dynamics.Thefaster arrow will decellerate faster due to the higher velocity while traveling down range,but if you assume impact with the same kinetic energy (bad assumption at longer distances), the penetration diferences will be minimalat best.In this it is assumed the arrows differ only in length and weight but not cross-sectional area. At a certain distance downrange the arrows will theoretically be going and decelerating at the same rate. Thus the lighter will have less kinetic energy down range.

Like I said I am a nerd and do this for a living.