A skier starts from rest at the top of a frictionless incline of height 20.0 m.
ID: 1332032 • Letter: A
Question
A skier starts from rest at the top of a frictionless incline of height 20.0 m. At the bottom of the incline, the skier encounters a horizontal surface where the coefficient of kinetic friction between the skis and the snow is 0.210. a.) Find the skier’s speed at the bottom b.)How far does the skier travel on the horizontal surface before coming to rest? A skier starts from rest at the top of a frictionless incline of height 20.0 m. At the bottom of the incline, the skier encounters a horizontal surface where the coefficient of kinetic friction between the skis and the snow is 0.210. a.) Find the skier’s speed at the bottom b.)How far does the skier travel on the horizontal surface before coming to rest? A skier starts from rest at the top of a frictionless incline of height 20.0 m. At the bottom of the incline, the skier encounters a horizontal surface where the coefficient of kinetic friction between the skis and the snow is 0.210. a.) Find the skier’s speed at the bottom b.)How far does the skier travel on the horizontal surface before coming to rest?Explanation / Answer
a) let v is the skier speed at the bottom
Apply energy conservation,
final kinetic energy = initial potential energy
0.5*m*v^2 = m*g*h
==> v = sqrt(2*g*h)
= sqrt(2*9.8*20)
= 19.8 m/s
b) Let d is the distance travelled by the skier before coming to rest.
Workdone by friction = loss of kinetic energy
Friction*d*cos(180) = -0.5*m*v^2
-mue_k*m*g*d = -0.5*m*v^2
d = 0.5*v^2/(mue_k*g)
= 0.5*19.8^2/(0.21*9.8)
= 95.25 m