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Question Number 97628 by peter frank last updated on 08/Jun/20

	Answered by Rio Michael last updated on 08/Jun/20

	$Assume the thickness of each piece = h and the$ $acceleration produced by each piece = a$ $from v_{f}^{2} - v_{0}^{2} = 2 a h \Rightarrow v_{0}^{2} = - 2 a h for reducing speed .$ $lets assume we have n pieces the v_{0}^{2} = - 2 n a h$ $\Rightarrow n = \frac{- v_{0}^{2}}{2 a h} . . . . . . (i)$ $The bullet losses \frac{1}{20} of its speed as it passes through the piece$ $so its final speed is given by : v_{f} = v_{0} - \frac{v_{0}}{20} \Rightarrow v_{f} = \frac{19 v_{0}}{20}$ $v_{f}^{2} - v_{0}^{2} = 2 a h but v_{f} = \frac{19 v_{0}}{20}$ $\Rightarrow {(\frac{19 v_{0}}{20})}^{2} - v_{0}^{2} = 2 a h$ $\frac{361 v_{0}^{2}}{400} - v_{0}^{2} = 2 a h$ $- \frac{39 v_{0}^{2}}{400} = 2 a h but from (i), 2 a h = - \frac{v_{0}^{2}}{n}$ $\Rightarrow n = \frac{- v_{0}^{2}}{- \frac{39 v_{0}^{2}}{400}} \Rightarrow n = 10.62, n \approx 11 pieces$
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