downhill skier starts skiing down from the top of a mountain from a height H. As
ID: 1311353 • Letter: D
Question
downhill skier starts skiing down from the top of a mountain from a height H. Assuming no frictional forces act on the skier until she reaches the bottom of the hill and comes to a safe stop, which one of the following statements is true?
-The skier's initial potential energy is equal to the skier's initial kinetic energy.
-The principle of conservation of mechanical energy does not apply as the skier is stopping.
-When the skier is halfway down the mountain, her speed is one-half of the speed she has at the bottom before friction begins to slow her down.
-The kinetic energy of the skier decreases as her gravitational potential energy decreases.
-When the skier is halfway down the mountain, her total mechanical energy is reduced to one-half its initial value.
Explanation / Answer
As ther is no non-conservative force(frictional force), hence the conservation of mechanical energy can be appled till the bottom of the mountain before friction starts acting .So intially
Total mechanical energy =Total potential energy=mgH
As the skier descends down the potential energy starts decreasing and the kinetic enegy starts increasing.
So none of the above statements is true . Velocity halfway is V= (gH)1/2 and the velocity at the bottom is (2gH)1/2
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