A) 30 cm
B) 40 cm
C) 10 cm
D) 50 cm
E) 20 cm
Correct Answer: C
Solution :
Let the velocity of the bullet when it strikes the target is \[v\]\[cm\,\,{{s}^{-1}}.\] After penetrating 30 cm, velocity becomes half i.e., \[\frac{v}{2}.\] From equation \[{{v}^{2}}={{u}^{2}}+2as\] \[\therefore \] \[{{\left( \frac{v}{2} \right)}^{2}}={{v}^{2}}+2a\times 30\] or \[-60\,a={{v}^{2}}-\frac{{{v}^{2}}}{4}\] or \[-60\,a=\frac{3{{v}^{2}}}{4}\] \[\therefore \] \[a=-\frac{{{v}^{2}}}{80}cm\,\,{{s}^{-2}}\] Let the bullet further penetrates x cm before coming to rest, therefore \[v{{}^{2}}=u{{}^{2}}+2as\] \[0={{\left( \frac{v}{2} \right)}^{2}}+2\left( -\frac{{{v}^{2}}}{80} \right)x\] \[\frac{{{v}^{2}}x}{40}=\frac{{{v}^{2}}}{4}\] \[x=10\,cm\]
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