I do not see any attempt at coding any collision. What have your tried?
Things I have noticed:
* class names should begin with uppercase characters (by convention)
* method names should begin with lowercase characters (by convention)
* the setting of the images for your cat, as coded, need to be read from file to create the image and then set every act method the cat moves; this is far from efficient and may cause lag; it would be far better to hold the images in fields and set the cat to the appropriate image only when a change in direction is detected. This means you would need three fields in the class -- two for the left and right facing images of the cat and one for the current direction the cat is facing
* the fall method is limited, as written; that is, the only vertical movement the cat can do right now is in the downward direction at a constant rate of 5 pixels per act cycle; a field can be used to hold a variable rate of falling. This will allow for the implementation of gravity and jumping (movement in the upward direction) as well.