What is the acceleration of a snowboarder when turning on a slope?

[rugalas]

Say a 70kg snowboarder is cruising straight down a hill at 20 mi/h. The slope of the hill is due south and at a 30 degree angle. The snowboarder sees a big tree ahead and turns his board 35 degrees to the right.

What is the snowboarders acceleration while going straight?
What is the snowboarders acceleration after having turned 35 degrees?


Thanks

 

[Tachyonie]

Are you including air resistance and friction of the snow?
PS: If this is your HW feel free to post it in the HW forum.

Tachyon.

 

[rugalas]

This is not for homework, I finished uni a few years ago. I'm just studying physics for myself and I have had a bit of difficulty conceptualising this particular problem. I'm not including air resistance, but friction, yes and no. No in the sense of friction slows you down depending on the friction coefficient. But sort of yes, because when the board is at an angle it seems to me the friction will vary along the edge of the board and this variance will of course affect the direction of the acceleration.

If the boarder is going straight down the incline(ignoring friction) here's what I'm getting:

Fgrav = m * g = (70 kg) * (9.8 m/s/s) = 686 N
Fparallel = 686 N * sin (30 degrees) = 343 N
acceleration = Fparallel / m = (343 N) / (70 kg) = 4.9 m/s/s, down the incline

Hopefully that's right. The problem is when the boarder turns 35 degrees to the right. Because although the slope is 30 degrees, the boarder is now facing an angle less than 30 degrees in terms of slope, and now there is a 35 degree angle between the board and Fparallel as well.

So here I have problems, how do you calculate the "slope" of the board? How do you calculate the force that gravity drags the board along the diagonal? What kinds of friction are there going to be at the front of the board and the forward facing side since they are now at an angle? If you know any online resources that would be great as well because all I find is stuff http://www.glenbrook.k12.il.us/gbssci/phys/Class/vectors/u3l3e.html" which deal with the 2d case and not 3d slopes.

Thanks