Why did my teacher assume that vf does not change upon landing in the last sub-question? This makes no sense to me. Is there such a way that the skier can change direction of vf without changing the magnitude of it? Otherwise, the skier will collide in an inelastic collision with the ground (since he does not bounce off) and this means that all the vertical velocity is lost. I would calculate vertical velocity of vf and use that to find work done.