Halliday, Resnick & Walker — Force and Motion-II: Problem 18

18 You testify as an expert witness in a case involving an accident in which car A slid into the rear of car B, which was stopped at a red light along a road headed down a hill (Fig. 6-24). You find that the slope of the hill is \(\theta = 12.0^\circ\), that the cars were separated by distance \(d = 30.0 \text{ m}\) when the driver of car A put the car into a slide (it lacked any automatic anti-brake-lock system), and that the speed of car A at the onset of braking was \(v_0 = 18.0 \text{ m/s}\). With what speed did car A hit car B if the coefficient of kinetic friction was (a) 0.60 (dry road surface) and (b) 0.10 (road surface covered with wet leaves)?