A speed skier is travelling horizontally at a constant speed of 5.80 m/s when she approaches a snow-covered hill that has a slope of 23.0° above the horizontal. The coefficient of kinetic friction between the skis and the hill is 0.350 and the combined mass of her and her skis is 77.0 kg. If she decided to glide up the hill, how far would she make it before she comes to a complete stop?
Fnet = m*a
Fk = μ Fn
Fg = m(-g)
Fgx = m(-g)sinθ
Fgy = m(-g)cosθ
The Attempt at a Solution
So first I solved for the y component of the force due to gravity:
Fgx = (77.0kg)(-9.8m/s2)*cos23 = -694.61296
Then I solved for the kinetic friction with the the y component of the gravity force equaling the normal force:
Fk = (0.350)(-694.61296) = -243.11454
Then I went on to solve for acceleration using the Fnet formula with the x component of gravity subtracting the kinetic friction force:
m*a = Fgx - Fk
(77.0kg)*a = [(77.0kg)(-9.8m/s2)*sin23] - 243.11454
a = -6.98650
I was just wondering is this right so far?