How fast is the skier moving at the top of the hill?

Question

A skier is initially moving at 18.1m/s on level ground as they approach a hill that is angled upward at 16.3 degrees. The skier then slides up the hill over a diagonal distance of 4.8m (assume a coefficient of friction of 0.1) how fast is the skier moving at the top of the hill?

Answer 1

You can solve this problem either by using forces and Newton's Second Law of Physics OR conservation of energy.

The latter concept gives us that the total work by non-conservative forces = change in kinetic energy + change in the potential energy of gravity.

Consider: you have both an initial and a final kinetic energy. Since KE = one-half times the mass times the square of the speed you can solve for the final speed once you find the final KE.

The change in the potential energy of gravity = mass times acceleration of gravity times the change in height = mgh. The geometry in this case is that you can find h from the length of travel (the hypotenuse of the triangle) and the angle at the base of the triangle.

Lastly you can use idea that work is the product of force and displacement and the cosine of the angle between them. The displacement is the length of travel. The force is that of friction (remember to solve for the normal force of the skier ON AN INCLINE. What is the angle between the two? Diagrams really help in physics problems!!