Final answer:
The inquiry pertains to the calculation of the time at which a ball reaches a given height during its flight, with factors like gravity affecting its vertical position and velocity. The question involves solving quadratic equations to find the relevant times and constructing graphs to visualize the ball's constant horizontal velocity and varying vertical velocity over time.
Step-by-step explanation:
The question involves calculating the time it takes for a ball to reach a certain height in its trajectory, considering its vertical position over time. By utilizing the provided quadratic equation and finding the roots, we are able to determine the positive root as the relevant solution, since it corresponds to the time after the ball has been launched. Additionally, concepts such as horizontal velocity and vertical velocity are applied to further analyze the ball's motion, including examining the graph of the ball's velocity over time and discussing the effects of gravity on its vertical velocity.
During its flight path, the ball is affected by gravity, which influences both its vertical position and its vertical velocity over time. The initial vertical velocity and the acceleration due to gravity (-9.8 m/s²) must be taken into account to accurately sketch the graph of the ball's velocity. References to Table 3.2 suggest examining the ball's motion at specific time intervals, which helps in understanding how the ball's velocity changes as it travels upwards and then downwards.
Considering the ball's flight in terms of horizontal velocity, the graph would depict a constant positive value, which indicates that there is no horizontal acceleration affecting the ball's motion in that direction—for instance, if air resistance is neglected.