Final answer:
The statement about a stretched bow and compressed rubber ball possessing elastic potential energy is true. However, the statement about a rock's kinetic energy increasing as it is thrown into the air and potential energy increasing as it falls to the ground is false; kinetic energy is converted to potential energy as it rises and back to kinetic energy as it falls.
Step-by-step explanation:
The statement that 'A stretched bow and a compressed rubber ball both possess elastic potential energy' is true. When a bow is stretched, the elastic potential energy is stored in its bent limbs as they strive to return to their original shape, and similar energy is stored in a rubber ball when it is compressed. Elastic potential energy is energy stored in an object due to its deformation, such as stretching or compressing.
For a rock thrown into the air, the statement in the question is false. When the rock is thrown upwards, its kinetic energy converts into gravitational potential energy as it rises. As it falls back to the ground, the gravitational potential energy is converted back into kinetic energy, not the other way around as stated in the question. Energy is conserved throughout this process as it merely changes forms from kinetic to potential and vice versa.