Final answer:
When the starting gun is fired for a race at the bottom of a hill, both kinetic and potential energy of the runners change. Kinetic energy increases as they start running and speed up, and potential energy increases as they ascend the hill. Therefore, the correct option is c) Both kinetic and potential energy.
Step-by-step explanation:
When the starting gun is fired for a cross country foot race at the bottom of a hill, the form of mechanical energy that will change for the runners is c) Both kinetic and potential energy. Initially, at the starting line, the runners have minimum kinetic energy because they are not moving.
However, once they start running, their kinetic energy increases as their speed increases. Moreover, as they run up the hill, they gain height, which increases their gravitational potential energy. Therefore, both kinetic and potential energy change during the race.
It's also important to note that at the bottom of the hill, the potential energy is at its minimum value and it will increase as the runners move uphill.
Likewise, the kinetic energy of the runners at rest is minimal but will increase as they accelerate. The mechanical energy during the motion changes as the runners' energies transform from potential to kinetic and vice versa throughout the race.