# Efficiency clarification question?

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Athletes who compete in downhill skiing try to lose as little energy as possible. A skier starts from rest at the top of a 65 m hill and skis to the bottom as fast as possible. When she arrives at the bottom, she has a speed of 23 m/s.

**My question is the following:**

Why is #W_"in" = ∆Eg# while #W_"out"# = #E_k# ? How do you know?

Athletes who compete in downhill skiing try to lose as little energy as possible. A skier starts from rest at the top of a 65 m hill and skis to the bottom as fast as possible. When she arrives at the bottom, she has a speed of 23 m/s.

**My question is the following:**

Why is

##### 1 Answer

Hope it answers.

#### Explanation:

Let

This is value of

The operative expression from the question is in bold text in the line below.

**as fast as possible**

Now kinetic energy which is converted from her original potential energy at the bottom of hill

Law of conservation of energy requires that change in potential energy and kinetic energy gained must be equal. However, from comparison of RHSs of equations (1) and (2), we see that these are not equal.

Evidently, some of potential energy has been lost in the process of skiing down the slope in terms of sliding friction and air friction.

As such this is value of

Efficiency