Asix 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?

PE=1/2 mV^2

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

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.