Use the work–energy theorem to prove that the speed of the mass at the bottom of the incline is the same as if it had been dropped from height , independent of the angle of the incline. Explain how this speed can be independent of the slope angle.

Question

Use the work–energy theorem to prove that the speed of the mass at the bottom of the incline is the same as if it had been dropped from height , independent of the angle   of the incline. Explain how this speed can be independent of the slope angle.

anonymous · Answer

In both cases work done by gravity will be same and = mgh , so the change in kinetic energy remains same, hence same speed .

anonymous · Answer

The gravitational only acts on a vertically downwards, regardless how you have moved, the difference in energy in only related to the difference in height. It's an conservative force. 
Thus, in both case, the equations written out are the same using the work-kinetic energy theorem, you just need to explain.