Is a book falling down from a high shelf kinetic or potential energy?

It's neither. It's just a piece of fruit.

While it's hanging and not moving, it has gravitational potential energy because of its position,

and food potential energy because of its chemical composition.

When it separates from the tree and moves to a different location, such as the ground or a

processing plant, it has kinetic energy because of its motion. Its chemical potential energy

doesn't change until it's processed, consumed, or rotted.