A 59 kg skier leaves the end of a ski-jump ramp with a velocity of 26 m/s directed 20° above the horizontal. Suppose that as a result of air drag the skier returns to the ground with a speed of 17 m/s, landing 11 m vertically below the end of the ramp. From the launch to the return to the ground, by how much is the mechanical energy of the skier-Earth system reduced because of air drag?

Question
Asked Oct 14, 2019

A 59 kg skier leaves the end of a ski-jump ramp with a velocity of 26 m/s directed 20° above the horizontal. Suppose that as a result of air drag the skier returns to the ground with a speed of 17 m/s, landing 11 m vertically below the end of the ramp. From the launch to the return to the ground, by how much is the mechanical energy of the skier-Earth system reduced because of air drag?

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Step 1

Consider the mechanical energy of the skier as the kinetic and potential energies, the mass of the skier be m, the initial velocity of the skier be u, the vertical displacement of the skier be h, the final velocity of the skier be v, the total initial energy of the skier be Ei, and the total final energy of the skier be Ef.

 

The total initial energy of the skier, when it is at the vertical height h, can be calculated as,

1
Е,
— тu* + mgh
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1 Е, — тu* + mgh

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Step 2

The total final energy of the skier, when it ret...

1
- ту
2
E, mgh
1
-ту? + mg(0)
2
1
— mу
2
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1 - ту 2 E, mgh 1 -ту? + mg(0) 2 1 — mу 2

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