A skier starts from rest at the top of a frictionless incline of height 20 m. At ...

Question

A skier starts from rest at the top of a frictionless incline of height 20 m. At the bottom of the incline, the skier encounters a horizontal surface where the coefficient of kinetic friction between the skis and snow is 0.210.
a. How fast was the skier going at the bottom of the incline?

b. How far does the skier travel on the horizontal surface before coming to rest?

 

Answers: 20m/s,97m

Answer 1

A skier starts from rest at the top of a frictionless incline of height 20 m. At the bottom of the incline, the skier encounters a horizontal surface where the coefficient of kinetic friction between the skis and snow is 0.210.
a. How fast was the skier going at the bottom of the incline?

b. How far does the skier travel on the horizontal surface before coming to rest?

Answers: 20m/s,97m

 

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a. the speed can be found from the balance of energies (potential and kinetic):

 

mgh=mv^2/2 ; v=sqrt(2gh)=sqrt(2*9.8*20)~20(m/s)

 

b. the distance is found from equalizing the wotk done by friction force to the energy of the skier:

 

mv^2/2=mg*S*0.21

 

S=V^2/2*1/(9.8*0.21)=97.2 (m)