Halliday, Resnick & Walker — Motion in Two and Three Dimensions: Problem 128

Chipsealing is a common and relatively inexpensive way to pave a road. A layer of hot tar is sprayed onto the existing road surface and then stone chips are spread over the surface. A heavy roller then embeds the chips in the tar. Once the tar cools, most of the stones are trapped. However, some loose stones are scattered over the surface. They eventually will be swept up by a street cleaner, but if cars drive over the road before then, the rear tires on a leading car can launch stones backward toward a trailing car (Fig. 4.42). Assume that the stones are launched at speed \(v_0 = 11.2 \text{ m/s}\) (25 mi/h), matching the speed of the cars. Also assume that stones can leave the tires of the lead car at road level and at any angle and not be stopped by mud flaps or the underside of the car. In terms of car lengths \(L_c = 4.50 \text{ m}\), what is the least separation \(L\) between the cars such that stones will not hit the trailing car?