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An energy analysis begins by first identifying which types of forces are doing net work upon the object. In the case of the sledder, frictional forces (friction and air resistance) are said to be negligible. The normal force acts perpendicular to the sledder's motion and does not do work upon the sledder. So gravity - a conservative force - is the only force doing work upon the sledder.
Since the only work being done on the sledder is being done by a conservative force, the total mechanical energy will be conserved. See Know the Law section. The amount of total energy - KE plus PE - at the beginning of the motion will be the same amount at every location along the path of the sledder. And of course at location E, there is no potential energy since the sledder is at ground level (much like at location C). Using these principles, all blanks can be determined.
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Energy Conservation:
If the only forces doing net work upon an object are conservative forces (such as gravity and spring forces), then the mechanical energy of the object will be conserved. The energy may change from one form to another - potential to kinetic or vice versa; but the total amount of the two forms together will be unchanging.
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