Answer
Initial potential energy = 71J
Kinetic energy before striking floor = 71J
Work Step by Step
Due to the conservation of Mechanical Energy Theorem, the Potential Energy + Potential Energy of an object must always equal a constant. Therefore, at this moment, the book has the same mechanical energy as it did when it was at the top of the shelf (initial). When it was at the top of the shelf, it had no kinetic energy because it was not moving so we have:
Initial potential energy + 0 = 47J +24J
Therefore, the initial potential energy was 71J.
By the same reasoning, when the book is just about to strike the floor, the height in mgh is 0 so the book has no more potential energy. However, the total mechanical energy must be constant so we have:
Kinetic Energy + 0 = 71J
or that the final kinetic energy is 71J
