Suppose someone caused a book to fall from the shelf to the ground. Compared to the total sum of kinetic and potential energy the book has while on the shelf, about how much would it have when it is halfway from the shelf to the ground? no energy, half as much, twice as much, or the same amount? Pretty easy question.

book resting on a shelf has no potential energy relative to the shelf since it has a height of zero meters relative to the shelf. However, if the book is elevated to some height above the shelf, then it has potential energy proportional to the height at which it resides above the shelf.

An object can have both kinetic and potential energy at the same time. For example, an object which is falling, but has not yet reached the ground has kinetic energy because it is moving downwards, and potential energy because it is able to move downwards even further than it already has. The sum of an object's potential and kinetic energies is called the object's mechanical energy.

As an object falls its potential energy decreases, while its kinetic energy increases. The decrease in potential energy is exactly equal to the increase in kinetic energy.

Another important concept is work.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y