Dear Student ,
14.(a) Here it does not violate the law of conservation of energy .You must know that if a body falls freely then its speed and kinetic energy both will increase .
Now you may think from where dos this kinetic energy come?
Look when a body falls freely then the potential energy is converted into kinetic energy and hence the sum of the energies remains constant through out the motion .So the energy is conserved .
(b) Now here look the energy applied by you is converted in to heat energy that's why you sweat .
But scientifically no work is done by you as the displacement of the huge rock is zero .
Regards