Why can an Arrow penetrate through sand better than a bullet? If you watch the accompanying video you will see an experiment where 3 different guns are fired at a box of sand. In each case the bullet stops well before it has a chance to exist out of the other side of the box. 
Next a man fires an arrow from a bow. The arrow travels straight through the box, with the head exiting the other side. 
Why is the arrow able to do what the bullet can not?
https://www.facebook.com/www.centraltexasbowhunter.net/videos/358725874321915/?hc_location=ufi
 A: A bullet designed to slow down inside an object, say a soft nosed round or equivalent, will disperse its greater kinetic energy inside the target. An arrow is not constrained by such a design, if it has sufficient kinetic energy, it will use all of it to pass through the  target. 
The bullet basically dumps most of its energy into the sand whereas the arrow does not flatten on impact. Its slower speed may be an advantage here and if it has the right amount of kinetic energy it can force the sand grains aside because of the shape of the arrow head.
EDIT In reference to my use of the word softnose, (or equivalent) rounds as in OON's comment below. Handguns are banned in my country and shotguns/rifles  are tightly regulated. So, TBH, what I actually know best about firearms is to stay well away from them.
I went through various sites regarding dum dum type bullets, sorry that's the British name, and the type of round I meant to base my answer on. I am not sure of other names for those bullets. I tried to discover how all rounds deform (whether designed to or not) once inside the target, a deer in most of the cases I read about. I suppose my basic point is that higher K.E is not necessarily better. The sand compacts in front of the round and increases it's cross-section. What I would like to know is more about the response of sand to impulse shock, but I couldn't find a source. Sorry I was not clear above. END EDIT
A: Think of the sand as a semi-viscus fluid.  The slower projectile speed of the arrow allows the sand to flow and accommodate it, while the higher velocity of the bullet limits the sand's ability to do the same.
