How do I find the coefficient of friction when given velocity, distance, and mass?

Question

A skier, moving at 8m/s, slides to a stop on a level surface while moving 64m. Assuming her mass to be 60kg, what is the coefficient of friction between her skies and the snow?

Answer 1

Let's say the skier is headed in the positive $x$ direction. Draw a free body diagram. The only non-negligible force in this direction will be due to friction, which we assume is constant: $f = -\mu N = -\mu m g$. By Newton's 2nd law, the sum of all forces in this direction gives $m a = -\mu m g$. This simplifies to $\mu = -a/g$. You need to find the acceleration. Use $v_f^2 - v_0^2 = 2a\Delta x$ to get $a = -v_0^2/2\Delta x$, giving a solution

$$\mu = v_0^2 / 2g\Delta x \approx 0.05 $$