Calculating Angle and Height in Conservation of Energy Problem with Friction

[TheMasterFool]

Homework Statement

A 46 kg skier slides down a slope 21.7 m long, incilned at an angle θ to the horizontal. The magnitude of the kinetic friction force is 41 N. The skier s initial speed is 0.65 m/s and the speed at the bottom of the slope is 7.19 m/s. determine the angle θ from the law of conservation of enegery. Air resistance is neglible

Homework Equations

PE=mgy, KE= 1/2mv^2, W=F*d, Ff=μmgsinθ

The Attempt at a Solution

My attemp at the equation was based on the law of conservation of energy with this resulting formula

(mgh+1/2mv^2-mgh-1/2mv^2)/Ff*d=sinθ

I can't figure out how to find the height without an angle or vice versa, i ve been trying to figure it out for the last little bit with no success. I feel like I m missing just one step

 

[PeterO]

Homework Statement

A 46 kg skier slides down a slope 21.7 m long, incilned at an angle θ to the horizontal. The magnitude of the kinetic friction force is 41 N. The skier s initial speed is 0.65 m/s and the speed at the bottom of the slope is 7.19 m/s. determine the angle θ from the law of conservation of enegery. Air resistance is neglible

Homework Equations

PE=mgy, KE= 1/2mv^2, W=F*d, Ff=μmgsinθ

The Attempt at a Solution

My attemp at the equation was based on the law of conservation of energy with this resulting formula

(mgh+1/2mv^2-mgh-1/2mv^2)/Ff*d=sinθ

I can't figure out how to find the height without an angle or vice versa, i ve been trying to figure it out for the last little bit with no success. I feel like I m missing just one step

How much work was done against friction during the slide?

 

[TheMasterFool]

Hey I think i figured it out, I took sin theta outta my energy conservation since it gave me the resisting force of 41N. I then used the energy conservation formula to find height and then O/H sin -1 to find my angle which turned out to be sig fig 12 degrees. It feels right but I guess I ll find out and post again.