A 60 kg skier travels 4 km along a slope at constant velocity, increasing their

Question

A 60 kg skier travels 4 km along a slope at constant velocity, increasing their elevation by 20 m. During this time, they experience a constant drag force of 30 N. They then jump a height of 2 m.

What is the minimum take off speed needed to make the jump?

What was the energy required to increase their elevation by 20 m?

What was the energy required to overcome the drag force?

The skier converts internal energy to work at 10% efficiency. Given the change in elevation and drag force, how much internal energy was required for the skier to ski along the slope?

Explanation / Answer

slope of incline = tan-1(20/4000)=0.286o

let the minimum take off speed be v

v=sqrt(2*9.8*2/sin20.286)=1252.2 m/s

take off speed = 1252.2 m/s

energy required to increase elevation by 20 m =(60*9.8*20)=11760 J

energy required to overcome the drag force = 30*4000=120000 J

total energy required to be overcome = 11760+120000=131760 J

efficiency=10%

internal energy required to overcome 131760 J=131760/0.1=1317600 J=1317.6 kJ

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