Question

State the law of conservation why is a person hit harder when he falls in a hard floor then he falls on sand in a same hieght

Answer 1

The law of conservation states the energy is neither created nor destroyed. Energy transforms from one form into another.  The total energy of a system remains constant, if there is no external force acting on the system.

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A person falling on the floor receives more injuries, as the floor is very hard substance. It offers lot of resistance to objects trying to penetrate into it.

If the person falls on the floor, the momentum (& speed) is brought to stop within a fraction of a second. Thus the impact on the head due to the floor is very very high.  (impact = change in momentum / time duration of contact).
Thus it pains a lot and serious injuries are also seen.

On the other hand, if a person falls into a heap of sand, then the looseness of the sand saves the person from injury. The sand caves in. The person's body moves into the sand a foot or more inside. That too uniformly.

  The impact is then is lower, as the time duration of contact during slowing down process is higher. So there will not be any injuries.