mechanics

The answer is C. (1) and (2) only.

(1) and (2): When Danny falls initially to the moment that it just reaches the lowest point, his mechanical energy is conserved. That is, in this period, his kinetic energy and gravitational potential energy interchange with each other.

When Danny falls from a higher position to a lower position, there must be a loss in gravitational potential energy of him, regardless of the position of the reference level. So, at the lowest point, his gravitational potential energy must be the lowest.

And as the gravitational potential energy is the lowest at the lowest point, and mechanical energy is conserved, so his kinetic energy must be the highest at this point.


(3): When Danny hits the ground and bounces up, his mechanical energy is not necessary conserved. It depends on the kind of collision it is. When the collision is perfectly elastic, then his mechanical energy is conserved. If it is inelastic, then his mechanical energy is lost as internal energy or sound energy.