How far will the skier slide before coming to a stop ?

Question

80-kg skier starts at rest at point A and skies down the slope on frictionless skies until they hit a rough patch on the flat ground after the 'bump'. Coefficient of kinetic friction = 0.5.

Answer 1

You do not give the starting height but let's assume it is h

The Potential Energy = mgh

Since the incline is frictionless, the kinetic energy at the bottom will be the same as the potential energy at the top =mgh

The friction force is given by f=(coefficient of kinetic friction) x (Normal Force) =mg/2

The distance traveled before stopping is d and in that time all of the work by friction will dissipate the total energy before hitting the rough surface

Work done by friction =-mgd/2

Therefore -mgh = -mgd/2

Distance traveled before stopping is 2h