Final answer:
Gravitational potential energy is proportional to mass and height, which is expressed in the formula P.E. = mgh. The joule is a derived unit of energy equivalent to kg m^2/s^2. A rock thrown into the air gains potential energy as it rises, and gains kinetic energy, not potential energy, as it falls.
Step-by-step explanation:
Gravitational potential energy is indeed proportional to both mass (m) and height (h) above a reference point. This is represented by the formula P.E. = mgh, where g represents the acceleration due to gravity. Therefore, it is true that potential energy increases with both mass and height.
Referring to a rock being thrown into the air, the increase in height does increase the rock's potential energy because it is getting farther from the Earth, which is the source of the gravitational field. Conversely, as the rock falls and velocity increases, its kinetic energy increases, not its potential energy. Therefore, the statement that an increase in velocity as it falls increases its potential energy is false; potential energy decreases as the rock falls.
The unit of energy, joule (J), is indeed equivalent to kilograms (kg) multiplied by meters squared per second squared (m^2/s^2). This unit derivation comes from the gravitational potential energy formula, where 1 Joule is the amount of work done when a force of 1 newton displaces an object by 1 meter. In terms of gravitational potential energy, since F = mg (force equals mass times acceleration due to gravity), the work done, or energy, is P.E. = mgh, where h is in meters, g is in m/s^2, and m is in kg, thus resulting in J = kg m^2/s^2.