posted by sarah .
Find the horizontal distance the skier travels before coming to rest if the incline also has a coefficient of kinetic friction equal to 0.23. (The incline makes an angle θ = 20.0° with the horizontal.)
Is there more information that goes with this problem? What is her initial speed before skiing up the incline?
A skier starts from rest at the top of a frictionless incline of height 20.0 m, as shown in the figure. As the bottom of the incline, the skier encounters a horizontal surface where the coefficient of kinetic friction between skis and snow is 0.23.
the skier's speed at the bottom is 19.8 m/s
and the skier travels on the horizontal surface before coming to a rest for 87.0 m
You seem to have answered your own question already, with the 87.0 meter dstance. I agree with the 19.8 m/s speed at the bottom, which equals
V = sqrt(2gH).
After that, work done agaisnt friction euqls kinetic energy at the bottom.
u*M*g*X = (1/2)M V^2
X = V^2/(2*u*g) = 87 m
u is the kinetic friction coefficient