Halliday, Resnick & Walker — Waves–I: Problem Problem_88

Figure 16.25b is a graph of speed \(v\) versus time \(t\) for a bullet of mass 10.2 g fired from a .38 Special revolver directly into body armor. The scales of the vertical and horizontal axes are set by \(v_s = 300 \text{ m/s}\) and \(t_s = 40.0 \text{ }\mu\text{s}\). Take \(v_l = 2000 \text{ m/s}\), and assume that the half-angle \(\theta\) of the conical dent is \(60^\circ\). At the end of the collision, what are the radii of (a) the thinned region and (b) the dent (assuming that the person wearing the armor remains stationary)?