Final answer:
The question is about calculating the stopping distance of a skier due to friction after landing on horizontal ground. This involves applying the work-energy principle to find the distance over which the kinetic friction acts to reduce the skier's kinetic energy to zero. The necessary physics concepts include kinetic energy, work done by friction, normal force, and the coefficient of kinetic friction.
Step-by-step explanation:
The student's question pertains to the calculation of the distance a skier moves after landing, considering the initial horizontal speed and the effects of friction.
This scenario falls under the principles of kinetic friction and motion in physics, specifically dealing with nonconservative forces and energy conservation.
When a skier lands and slides to a stop, the work done by friction is what brings them to rest. We can apply the work-energy principle, which states that the work done by forces (other than conservative forces) is equal to the change in kinetic energy of the object.
To find the distance the skier moves, we can use the following equation derived from the work-energy theorem:
W = ΔKE,
where W is the work done by friction and ΔKE is the change in kinetic energy. The work done by friction is equal to the force of friction (f k) multiplied by the distance (d) over which it acts, and the kinetic energy change is the difference between the initial and final kinetic energies. Since the skier comes to a stop, the final kinetic energy is zero.
The coefficient of kinetic friction (μk) between the skier's skis and snow can be calculated using the formula f k = μk N, where N is the normal force which, on flat ground, is equal to the gravitational force (weight) of the skier. The initial kinetic energy (KEi) can be determined with KEi = (1/2)m vi2, where m is the skier's mass and vi is the initial speed.
By setting the work done by friction equal to the initial kinetic energy and solving for the distance d, the skier's sliding distance can be determined. It is important to note that the normal force on a horizontal surface is simply the weight of the skier, which is the mass (m) multiplied by the acceleration due to gravity (g).