Final answer:
The drag force proportional to v² significantly alters a baseball's ascent and descent by opposing its motion and reducing its speed more rapidly than gravity alone, illustrating an application of Newton's second law.
Step-by-step explanation:
The impact of the drag force being proportional to v² on a baseball's motion as it ascends and descends is significant in influencing its speed during flight. When the baseball is thrown upwards, the drag force works against the upward velocity, reducing its speed more rapidly than gravity alone would. This is because as the baseball's speed increases, the magnitude of the drag force increases as well. Conversely, when the baseball begins to fall back down, the drag force continues to oppose the motion, this time decelerating the baseball on its descent and potentially preventing it from reaching the same speed it had upon release (assuming no other energy losses).
In both scenarios, the drag force contributes to a net force on the baseball that opposes the direction of motion, resulting in a change in the motion described by Newton's second law. Especially if the baseball reaches high speeds, the drag force can be a major factor in the overall dynamics of the baseball's flight, illustrating an interesting application of fluid dynamics.