You say to yourself "Self ! Energy can't be created or destroyed.
The skier's kinetic energy at the bottom of the hill is exactly the
potential energy s/he had at the top."
Potential energy at the top = (mass) (gravity) (height)
= (65.8 kg) (9.8 m/s²) (521 m)
= (65.8 x 9.8 x 521) kg-m²/s²
= 335,961.6 joules .
Part-a: No energy is lost on the way down.
Kinetic energy at the bottom = (1/2) (mass) (speed²)
335,961.6 joules = (1/2) (65.8 kg) (speed²)
335,961.6 joules / 32.9 kg = speed²
335,961.6 kg-m²/s² / 32.9 kg = speed²
(335,961.6 / 32.9) m²/s² = speed²
speed = 101 m/s
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Part b: Energy is lost on the way down.
Just subtract the 1.4 x 10⁵ J of energy away from the 335,961.6 J
before you do the Kinetic Energy calculation at the bottom of the hill.
The skier lost that much energy on the way down, by scraping against
snow and air and stuff, so it isn't available to make speed at the bottom.
