A 60-kg skier starts from rest at the top of a 80-meter high practice slope (A). He uses his poles to propel himself forward, doing 12000 Joules of positive work from the top of the hill to the halfway point on the hill (B). Use g = 10 m/s/s to perform an energy analysis

Explanation:

Given data

Mass of skier m=65kg

Height of slope =80m

Potential energy possessed by the skier (positive work done) =12000J

Analysing his energy at half way point on the hill

Potential energy will be equal to kinetic energy

Applying the conservative principles of energy when the skier is at half way point in the hill

I.e

mgh= 1/2mv²

The masses will cancel out

gh=v²

Given g= 9.81m/s²

Let's solve for the velocity

v²=9.81*80

v=√784.8

v=28.0m/s

Now we can solve for the kinetic energy

KE= 1/2mv²

KE =1/2*60*28²

KE =47063.9/2

KE=23531.9J

Hence we can calculate the energy gained by the skier during his movement

Energy gained = KE-PE

= 23531.9-12000

= 11531.9J