Final answer:
The subject matter is physics, specifically relating to the calculations of free fall and kinematic equations. The problems involve finding distances fallen and final velocities of objects under the influence of gravity.
Step-by-step explanation:
The questions provided pertain to the calculations related to free fall and kinematic equations in physics. They involve understanding the motion of objects under the influence of gravity, calculating distances fallen, final velocities, and the effects of acceleration. When an object is dropped from a certain height, its distance traveled and velocity change over time, according to the equations of motion under gravity. For example, using the provided information, one can find the distance an object falls in the first second of free fall by using the simple kinematic equation d = 1/2 * g * t2. In this case, for a time 't' of 1 second and the acceleration due to gravity 'g' as 9.8 m/s2, the calculation would be d = 1/2 * 9.8 * 12, giving us 4.9 meters. Similarly, to determine the final velocity right before impact, one utilizes the kinematic equation v = √(vo2 + 2ad), where 'v' is the final velocity, 'vo' is the initial velocity, 'a' is the acceleration, and 'd' is the distance fallen. By substituting known values, we find the final velocity.