Work (Conservation of Energy/Newton's Laws)

[jzwiep]

Homework Statement

MP 11.44

Sam, whose mass is 75kg, straps on his skis and starts down a 50-m-high, 20degree frictionless slope. A strong headwind exerts a horizontal force of 200N on him as he skies. Find Sam's speed at the bottom (a) using work and evergy (b) Using Newton's laws

Homework Equations

v²=v₀² + 2ad

Dot product

The Attempt at a Solution

(a)

U = K + W_Headwind

v_f=sqrt(2*(mgh+F*(h/sin20)*cos(160))/m)

Which got me= 15.7270m/s

(b)

F_net = F_g - F_headwind
a=(mgsin(20)-200/cos(20))/m

v²=v₀² + 2ad
v= sqrt(2ad)

Which got me: 12.225m/s

I'm not sure where I went wrong. Any thoughts?

 

[Doc Al]

F_net = F_g - F_headwind
a=(mgsin(20)-200/cos(20))/m

What's the component of the 200N force parallel to the slope?

 

[ashishsinghal]

200/cos(20) means that component of force along the slope is greater than the force itself!
You should write 200*cos20. Well, maybe it is just a typing error (like evergy) because you wrote mg*sin20 and not mg/sin20

 

[jzwiep]

Thanks. I drew the triangle backwards.