Question

A bullet fired from a rifle loses $ 20\% $ of its speed while passing through a wooden plank. Then, minimum number of wooden planks required to completely stop the bullet is

• A. 3
• B. 5
• C. 15
• D. 25

Answer 1

Answer: (A)

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 2 nd 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 3 rd block
$v_{n}=\left(\frac{4}{5}\right)^{n} v$
For $v_{n} \rightarrow 0, n \rightarrow \infty$
Minimum value of 22 given in the question is $n=3$.