Final answer:
The height of a ball post-bounce depends on initial conditions and physics factors such as elasticity and gravity, making the initial statement True. Energy transformations during the motion of objects adhere to the conservation of mechanical energy, and the acceleration due to gravity is constant regardless of objects' initial velocities.
Step-by-step explanation:
The formula to find the height of the ball after n bounces is indeed dependent on factors such as initial height, elasticity, and gravitational acceleration, making the statement True. When a rock is thrown into the air, throwing it higher indeed increases its potential energy. As it falls, the potential energy is converted back into kinetic energy, not the other way around, thus the correct response is False. In terms of energy conservation, a ball at the top of a hill will have its maximum gravitational potential energy. As it rolls down the hill without friction, this potential energy is converted into kinetic energy, giving the ball its velocity at the bottom of the hill, which can be calculated using the principle of conservation of mechanical energy or appropriate kinematic equations.
To illustrate, a bungee jumper at the start of the jump has maximum gravitational potential energy, which is transformed into elastic potential energy at the bottom of the jump, perfectly demonstrating the energy transformation principles. If a superball is dropped and bounces back to its initial height with no loss of energy, it is an example of an ideal system with no energy loss.
For a student designing an experiment to show that acceleration is independent of an object's velocity, they would need to collect information such as the time taken for each ball to reach the ground and the distance traveled horizontally (if applicable). By comparing these measurements, they could demonstrate that acceleration due to gravity is constant, regardless of the initial velocity of the object.