Final answer:
The question involves using conservation of energy principles to analyze the motion of a 0.50-kg ball thrown at a speed of 12 m/s at an upward angle, including calculations of kinetic energy, potential energy, and total mechanical energy throughout its flight.
Step-by-step explanation:
The question pertains to the concept of conservation of energy in physics, specifically addressing the motion of a projectile. When a 0.50-kg ball is thrown with a speed of 12 m/s at an upward angle, energy conservation principles can be used to predict various aspects of its motion, such as velocity at different points, maximum height reached, and the work done by non-conservative forces if applicable. To solve such problems, one would typically separate the ball's initial kinetic energy into horizontal and vertical components, equate those to the potential and kinetic energy at the highest point of its trajectory, and account for energy changes caused by external factors like air resistance if they cannot be ignored. The kinetic energy, potential energy, and total mechanical energy at various points during the ball's flight can all be calculated using the conservation of energy theory.