To determine the work done on the ball by the gravitational force, we need to consider the change in gravitational potential energy as the ball moves between different points.
(a) The lowest point: At the lowest point, the ball is at its maximum height. The gravitational potential energy at this point is zero because it is taken to be zero at the initial point. Since the ball is moving downwards, the work done by gravity is negative. Therefore, the work done on the ball by the gravitational force at the lowest point is 0 J.
(b) The highest point: At the highest point, the ball is at its minimum height. The gravitational potential energy at this point is equal to the gravitational potential energy at the initial point because the ball-Earth system is taken to have zero potential energy at the initial point. Again, since the ball is moving upwards, the work done by gravity is negative. Therefore, the work done on the ball by the gravitational force at the highest point is 0 J.
(c) The point on the right level with the initial point: At this point, the ball is at the same height as the initial point. The gravitational potential energy at this point is equal to the gravitational potential energy at the initial point. Since the ball is not moving vertically, the work done by gravity is zero. Therefore, the work done on the ball by the gravitational force at this point is 0 J.
(d) The lowest point: The gravitational potential energy at the lowest point is zero because it was taken to be zero at the initial point.
(e) The highest point: The gravitational potential energy at the highest point is equal to the gravitational potential energy at the initial point because it was taken to have zero potential energy at the initial point.
(f) The point on the right level with the initial point: The gravitational potential energy at this point is equal to the gravitational potential energy at the initial point because it was taken to have zero potential energy at the initial point.
Therefore, the gravitational potential energy remains the same at all points - 0 J.