A) \[3\]
B) \[5\]
C) \[15\]
D) \[25\]
Correct Answer: A
Solution :
Let n number of wooden planks are required to Completely stop the bullet. Speed of the bullet after passing through 1 st block \[{{v}_{1}}=v-v\times \frac{20}{100}=v-\frac{v}{5}=\frac{v}{5}v\] Speed of the bullet after passing through 2nd block \[{{v}_{2}}=\frac{4}{5}\left( v-\frac{v}{5} \right)={{\left( \frac{4}{5} \right)}^{n}}v\] Similarly, speed of the block after passing through 3rd block \[{{v}_{n}}={{\left( \frac{4}{5} \right)}^{n}}v\] For \[{{v}_{n}}\to 0,\,\,n\to \infty \] Minimum value of 22 given in the question is\[n=3\].
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