Final answer:
The question is about the time a ball takes to return to the ground when tossed vertically upward, which involves physics concepts of projectile motion and kinematics to calculate the time of flight based on the initial velocity and displacement.
Step-by-step explanation:
The student's question pertains to the length of time in seconds it takes for a ball to return to the ground when tossed vertically upward. This is a concept related to Physics, specifically the study of projectile motion and free fall within the realm of classical mechanics. The important aspect to recognize is that the motion of the object is symmetrical in time during its ascent and descent if air resistance is neglected. The ball takes the same amount of time to rise to its highest point as it does to fall back down to its original launch level.
When dealing with projectile motion and determining the length of time the projectile will be in the air, the initial vertical velocity and the displacement from the starting altitude are critical. In the given examples, initial vertical velocities are provided along with the final positions of the ball relative to the starting point. Utilizing kinematic equations, which are a part of the basic principles of Physics, one can calculate the time the ball spends in the air before it returns to the ground.
For instance, a ball with an initial vertical velocity of 14.3 m/s that lands 20.0 m below its starting altitude will spend 3.96 seconds in the air. Similarly, a projectile that has an initial vertical velocity of 21.2 m/s and lands 10.0 m below its starting altitude will spend 3.79 seconds in the air. Thus, the calculation of the time of flight involves applying the appropriate kinematic equation to solve for the time variable 't'.