Question

the skier on reaching the bottom of the slope? A 60-kg skier starts from rest from the top of a 50-m high slope. If the work done by friction is -6.0 kJ, what is the speed of the skier on reaching the bottom of the slope? 17 m/s 31 m/s 28 m/s 24 m/s

Answer 1

Answer:

31 m/s

Step-by-step explanation:

In order to find the speed of the skier at the bottom of the slope, you have to apply the Work-Energy Principle for mechanical energy.

W ncf= ΔEm

Where ΔEm is the variation of mechanical energy between two points of the displacement and Wncf is the work of all non-conservative forces.

The only non-conservative force producing work is the friction force. The normal force doesn't produce work because it's perpendicular to the displacement.

The variation of the mechanical energy can be considered from the top to the bottom of the slope.

Wncf= Emf-Emi

Where Emf is the final mechanicl energy and Emi is the initial mechanical energy.

The mechanical energy is defined by:

Em= Ep+Ek

Where Ep is the potential energy and Ek is the kinetic energy.

At the top of the slope, there's only potential gravitational energy (the kinetic  energy is zero because the skier starts from rest)

Emi=Ep= mgh

m=60 kg, g=9.8 m/s² and h=50 m

Emi= 29400 J

At the bottom of the slope, there's only kinetic energy (the potential gravitational energy is zero because the height is zero)

Emf= Ek = 1/2mv² =30v²

where v is the speed and m is the mass.

Replacing in the equation:

-6.0 = 30v² - 29400

Solving for v (Adding 29400, dividing by 30, extracting the square root)

v=31.3 m/s