Final answer:
The greatest potential energy of a thrown ball is at its highest point, which can be calculated with the formula PE = mgh, with height being the crucial variable. The principles of conservation of energy enable calculation of potential energy, velocity, and heights in various scenarios.
Step-by-step explanation:
The ball will have the greatest potential energy at the point where it reaches its highest height in its path. This is because potential energy is dependent on the height of the object above the ground and is calculated using the formula PE = mgh, where m is mass, g is the acceleration due to gravity, and h is the height. Therefore, the correct answer to the question is (b) when the ball reaches its highest point.
The potential energy of the ball when it has fallen 3 m would depend on its mass and the height from which it was dropped. The velocity of the ball when it hits the ground can be calculated by using the principles of conservation of energy or the equations of motion. Similarly, the gravitational potential energy of a ball at the top of a hill and its velocity at the bottom can be found using the same principles, assuming no friction is involved. For the bullet, the maximum height reached can also be determined using the conservation of mechanical energy.
It is important to remember that at the highest point, the velocity of the ball is zero, and therefore, it has no kinetic energy at that moment, meaning all of its mechanical energy is in the form of potential energy.