Solve a Skier Work Physics Problem on a 37.2° Slope – No Friction

[Momentum09]

A skier of mass 72.6 kg is pulled up a slope by a motor-driven cable. How much work is required to pull the skier 64.3 m up a 37.2 degrees slope? (assumed frictionless) at constant speed of 63.2 m/s.

For this question, would I just use the equation W = 1/2 mv squared?

Thank you so much!

 

[Vagrant]

it is gaining height too, so PE=mgh is needed too

 

[gabee]

The velocity is not constant here.
I would use W=f.d

"...at constant speed of 63.2 m/s."

No--the equation K = (1/2)mv^2 is for kinetic energy. In your problem, the skier's kinetic energy remains the same because his speed remains the same. Only his gravitational potential energy (U = mgh) changes. Since the work done pulling the skier up does not go to changing his kinetic energy, it must have gone to changing his gravitational potential energy, right?

 

[Momentum09]

Oh I see! Thank you very much for your help!