Final answer:
The maximum height a stone reaches when projected vertically with a constant drag force cannot be precisely determined without additional information about the drag force.
In an ideal situation without drag, maximum height can be calculated using energy conservation principles. However, with drag, more complex calculations or numerical methods are needed.
Step-by-step explanation:
The question asks about the maximum height reached by a stone that's projected vertically with a constant drag force acting on its flight. In a real-world scenario without air resistance, using the principle of conservation of energy, we could calculate the maximum height using the initial kinetic energy being converted to potential energy at the highest point.
However, because a constant drag force is acting on the stone, the scenario is different. The drag force does work against the motion of the stone, dissipating some of the mechanical energy as the stone rises, which results in a lower maximum height than would be predicted by an ideal physics model with no air resistance.
Without the specific value of the drag force or a formula for how it changes with velocity, we can't provide an exact numerical answer for the maximum height.
In situations with air resistance or drag, the height can be determined by solving the equations of motion for the specific drag force involved, or using numerical methods if the force is complex.
For comparison, if air resistance is neglected, like when using energy considerations on the moon as in a provided example, a rock launched at an initial velocity of 12 m/s would have a complete transformation of potential energy into kinetic energy as it returns to the ground, making it easier to predict the motion using conservation of energy.
In the absence of air resistance, another example from a student question reveals that a ball thrown straight up with an initial velocity of 20 m/s would reach a maximum height of approximately 20.4 meters.
Similarly, a ball kicked with initial velocities of 16 m/s horizontally and 12 m/s vertically would have its maximum height calculated from the vertical component of velocity, assuming no air resistance.