A 60.0 kg skier is moving at 6.15 m/s on a frictionless, horizontal snow-covered plateau when...

A 60.0 kg skier is moving at 6.15 m/s on a frictionless, horizontal snow-covered plateau when she encounters a rough patch 3.95 m long. The coefficient of kinetic friction between this patch and her skis is 0.330. After crossing the rough patch and returning to friction-free snow, she skis down an icy, frictionless hill 2.95 m high.

How fast is the skier moving when she gets to the bottom of the hill?

How much internal energy was generated in crossing the rough patch?

Solutions

Expert Solution

Given,

mass of the skier (m) = 60 kg
initial speed (u) = 6.15 m/s
height (h) = 2.95 m
coefficient of kinetic friction () = 0.330
distance in horizontal direction (d) = 3.95 m

Also, acceleration due to gravity (g) = 9.8 m/s²

We know that,

Kinetic Energy,

OR, .................................... equation (1)

OR, ..................................... equation (2)

Equating equations (1) and (2)

We get,

Hence, the skier is moving at a speed of 7.96 m/s when she gets to the bottom of the hill.

The internal energy that was generated can also be referred to as gravitational potential energy which is given as,

Hence, the internal energy that was generated in crossing the rough patch is 1734.60 J.

genius_generous answered 1 week ago

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