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A bullet fired into a plank loses half of its velocity after penetrating a thickness of $3 cm$. assuming that it has constant force of resistance, how much further does it penetrate before coming to rest

\[(a)\;4\;cm\quad (b)\;3\; cm \quad (c)\;2\; cm \quad (d)\;1\;cm\]

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1 Answer

Let 'u' be initial velocity
$\bigg(\large\frac{u}{2}\bigg)^2$$-u^2=-2a \times 3$
Since it loses half its velocity after 3 cm
or $a=\large\frac{u^2}{8}$
Let x be the further distance to which it penetrates
Therefore Total distance $=x'=3+x$
$0-u^2=-2 \large\frac{u^2}{8}$$x'$
Therefore $x=4-3=1\; cm$
Hence d is the correct answer.
answered Jun 28, 2013 by meena.p
edited Mar 26, 2014 by balaji.thirumalai

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