Kinetic energy = (1/2) (mass) (speed)²
The rock's kinetic energy is not
(1/2) (4 kg) (10 m/s)²
= (1/2) (4 kg) (100 m²/s²)
= 200 Joules .
It may be more, or it may be less. The only thing
we can be sure of is that it is not 200 Joules.
It depends on where the cat is applying the force and how much the force is .. after all where and at what is distance from the axis of rotation of the door