Calculating Velocity of Snowboarder Down Slope

[GoSS190]

Need to find the equation for the velocity of a snowboarder going down a slope about to hit a jump. I know that the potential energy for going down the hill is mgh and that friction depends on the normal force which is mgcos(theta) and the distance going down the slope. I need to figure out what the equation for finding the opposing energy that is being produced by friction. I am looking to find the velocity at the bottom for all values of theta.

The known variables are..
m=100 kg
g=9.8 m/s^2
d=100 meters or the hypotenuse of the hill
mu (k)=.05

 

[tiny-tim]

Hi GoSS190!

Combine conservation of energy with the work-energy theorem …

energy "lost" to friction = work done by friction.