Answer to Question #102179 in Mechanics | Relativity for ddd

Question

A 59.3 kg skier is at rest at the top of a 346 m high run. The slope is inclined at a 15.9º angle relative to horizontal. Assuming that there is no friction between the skis and the snow, how much mechanical energy does the skier have when he/she is half way down the slope?

Answer 1

The total mechanical energy at the top of the slope is equal

$$E=mgh$$ $$=59.3\:\rm kg\times 9.8\: N/kg\times 346\: m=201\:000\;J.$$

Since there is no friction between the skis and the snow, the total energy is conserved. Hence, at the halfway down the slope the skier have the same amount of energy as at the beginning of motion.