Sam, Whose mass is 75kg(Work Energy Problem)

[Naomi]

Sam, whose mass is 75kg, starts down a 50-m-high, 20 degree frictionless slope. A strong headwind exerts a horizontal force of 200N on him as he skies. Use work and energy to find Sam's speed at the bottom.

Hi! I'm new to posting on this website but thought I'd give it a go! I would really appreciate help with this problem. I know the answer is supposed to be around 16m/s, but for some reason I am getting an answer that is too high of a velocity. Here is my attempted solution.

W = ΔKE+ΔU
Given he starts from rest, we know that,

W=KEf+Ui

Fx=200N
W=200N(50/tan(20))

200N(50/tan(20))=1/2mvf^2 -mghi

1712.6=Vf^2
Vf=√(1712.6) =41m/s

However, this solution is not correct. Where did I go wrong?

 

[Drakkith]

Thread has been moved from the General Physics forum.

 

[haruspex]

200N(50/tan(20))=1/2mvf^2 -mghi

have another think about that. Which term supplied energy, and which terms absorbed it?

 

[Naomi]

Okay, I re-solved the problem and got the correct answer. My method seemed to be correct. However, when I initially solved the problem, i did not account for the direction of the headwind (going against Sam). Because of this, I was getting an incorrect answer. Re-solved, my solution looked more like this:
W = KEf-Ui
W= 1/2mVf^2-mghi
W+mghi= 1/2mVf^2
Vf= sqrt((W+mghi)/(.5m))

My formula was correct initially, however I had to solve it with W being (-200N)(50/tan(20)), or -27474 rather than +27474 and all other values remaining the same.Thank for the help! The response definitely prompted me to look at second look at the problem from a different standpoint!