Calculating Work to Pull a Skier Up a Slope at Constant Speed

[Sheneron]

Homework Statement

A skier of mass 69.5 kg is pulled up a slope by a motor-driven cable.
a) How much work is required to pull him a distance of 59.1 m up a 30.1° slope (assumed frictionless) at a constant speed of 2.07 m/s?

The Attempt at a Solution

I started out this problem by finding out what that force of gravity parallel to the slope would be.
mgsin(30.1)=341.57 N

Then I figured I would find the total negative work that would be done for the whole slope so I multiplied that by 59.1m to get 20.186 kJ.

The thing I am not sure how to figure out is how much work is required to pull him up at 2.07 m/s. Because anything greater than 20.186kJ would just pull him up, but not necessarily at 2.07 m/s.

Also this answer alone counts as the right answer, but it can't be exactly right because its hasn't taken into account the desired velocity right?

 

[Runelord]

You did the problem absolutely right, the 2.07 m/s was just thrown in there to trick you. Because it is at a constant speed, Newtons Second Law says the forces must be equal. The 2.07 was an arbitrary value that the skier is brought to before the incline, it could have been 1000 with the same result.

 

[Sheneron]

I kind of had the inclination the whole time. So, it wouldn't matter what velocity he was traveling it would still be the same joules?