Question

A skier (m = 60 kg) initially at rest skis down a (frictionless) hill from an altitude of 75 m. When she reaches the bottom (a flat horizontal surface with µk = 0.2) she slows down until she comes to a stop.

(a) What is her speed when she reaches the bottom of the hill?

(b) Over what distance at the bottom does she come to a stop?

Answer 1

a ) The mass of the skier is m = 60 kg , and the height of the hill is 75 m

from The conservation of energy ,

the potential energy at the top when at rest is converted into kinetic energy

so.

potential energy PE = m.g.h , where mass m , accln due to gravity is g , and height is h

kinetic energy is

so ,

putting the values we get the speed of the skier at the bottom of the hill be v = 38.34 m/s

b) The friction force is given by

hence the retardation produced due to friction is given by

putting the value we get

The initial velocity of the skier is u = 38.34 m/s

The final velocity of the skier is v = 0 m/s

the distance over which the skier had stopped is d

so d is given by

putting the value we get the distance d = 375 m