Why could you hold a stack of books on your head without pain, whereas it would hurt if someone put a small pebble between the book and your head? Why is it so easy to cut yourself with the edge of a piece of paper (a "paper cut")?

Both the cases deal with the principle of pressure due to force acting on an area.

Explanation:

When a stone is place between a pile of book and our head when we carry it then the area subjected to the force decreases while the magnitude of the force remains same and therefore the pressure on our head increases.

As we know that pressure is force per unit area is called pressure.

Mathematically:

It is easy to cut our skin with an edge of a paper because our skin is relatively softer than the edge of a paper and the edge of a paper is thin which applies more pressure due to  less area of contact with our skin.

the answer is to check all of them! they all apply well at least i think so!

distance = 150m

displ = root (50 ^2 + 100^2)

root(2500+10000)

root 125000