Question

A skier starts from rest at the top of a hill that is inclined at 9.8° with respect to the horizontal. The hillside is 240 m long, and the coefficient of friction between snow and skis is 0.0750. At the bottom of the hill, the snow is level and the coefficient of friction is unchanged. How far does the skier glide along the horizontal portion of the snow before coming to rest? m

Answer 1

L = Length of the hillside = 240 m

m = mass of the skier

= Coefficient of friction = 0.0750

F_nhill = Normal force acting on the hill = mg Cos

f_hill = frictional force acting on the hill = F_nhill = mg Cos

F_n = Normal force acting on the horizontal surface = mg

f = frictional force on horizontal surface = F_n = mg

d = distance traveled on horizontal surface

Using conservation of energy

Gravitational potential energy at the top = work done kinetic friction on hill + work done on horizontal surface

mgL Sin = f_hill L + f d

mgL Sin = mg Cos L + mg d

gL Sin = g Cos L + g d

L Sin = Cos L + d

(240) Sin9.8 = (0.0750) Cos9.8 (240) + (0.0750) d

d = 308.2 m