Halliday, Resnick & Walker — Force and Motion–II: Problem 100

Car on an icy hill—destined for YouTube video. Some of the funniest videos on YouTube show cars in uncontrolled slides on icy roads, especially icy hills. Here is an example of such a slide. A car with an initial speed \( v_0 = 10.0 \text{ m/s} \) slides down a long icy road with an inclination of \( \theta = 5.00^\circ \) (a mild incline, nothing like the hills of San Francisco). The coefficient of kinetic friction between the tires and the ice is \( \mu_k = 0.10 \). How far does the car take to slide to a stop if we assume that it does not hit anything along the way?