Question

how is mechanical energy conserved when a ball is dropped from a height?

Answer 1

At the highest point before being dropped, the ball only has gravitational potential energy. While it is being dropped, it has both, kinetic and gravitational potential, because it is in motion. At the instant right before it hits the ground, the ball has only kinetic energy, this is because height is so negligible above the ground that it is taken as zero. After hiting a surface, some energy is converted to other forms such as heat, or light energy. Thus, this supports the theory of conservation of energy.