Final answer:
The questions cover various principles of physics including projectile motion, free fall, and Newton's laws of motion. Kinetic and potential energy conversion, the concept of displacement, and recoil velocities are addressed with explanations being provided as to why the given statements are false. So, the correct option is B.
Step-by-step explanation:
The questions provided relate to concepts in physics, specifically projectile motion, Newton's laws of motion, and the behavior of objects in free fall. In the given context, the scenarios describe instances where objects move under the influence of gravitational force alone or experience forces that obey Newton's third law. For the question whether increased height would increase a rock's kinetic energy, the correct answer is False. As a rock rises, its kinetic energy is converted to potential energy, and as it falls, its potential energy converts back to kinetic energy. The displacements described in the question about walking are equal for both persons because displacement is independent of path; it's determined solely by the change in position. Therefore, that statement is also False.
Regarding recoil, without additional information on mass or velocity involved, only a general principle can be stated: if two people push against each other, they will experience recoil velocities that are inversely related to their masses. Similarly, objects in projectile motion do not fall at different rates because of their initial velocities; they fall at the same rate due to gravity, which means that statement is also False.