A 61.0 skier is moving at 6.15 on a frictionless, horizontal snow-covered plateau when she encounters a rough patch 3.55 long. The coefficient of kinetic friction between this patch and her skis is 0.350. After crossing the rough patch and returning to friction-free snow, she skis down an icy, frictionless hill 3.35 high. How fast is the skier moving when she gets to the bottom of the hill? How much internal energy was generated in crossing the rough patch?