A six kilogram cat is resting on top of of book shelf that is one meter high. what is the cats potential energy relative to the floor?

The formula for Gravitational Potential Energy is: mass * g * height. The (g) is specific to the planet in which you're calculating in, which, assuming you mean a cat on Earth, is 9.8 m/s^2. The height is 1, and the mass is 6. Therefore, inputting that into the equation will give you:

6 * 9.8 * 1,

potential energy = 58.8J; correct to 3 significant figures.

PE=1/2 mV^2

replace the values in the above formula, and you'll get your answer