Question

A bullet looses $\left(\frac{1}{n}\right)^{th}$ of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be :

• A. $\frac{n^{2}}{2n - 1}$
• B. $\frac{2n^{2}}{n - 1}$
• C. Infinite
• D. n

Answer 1

Answer: (A)

$\frac{n^{2}}{2n - 1}$

Answer 2

$\left(1-\frac{1}{ n }\right)^{2} V ^{2}= V ^{2}-2 as$
$2 as = V ^{2}\left(1-\left(\frac{ n -1}{ n }\right)^{2}\right)= V ^{2}\left(\frac{2 n -1}{ n ^{2}}\right)$
$O = V ^{2}-2 ans$
$n =\frac{ V ^{2}}{2 as }=\frac{ V ^{2}}{ V ^{2}\left(\frac{2 n -1}{ n ^{2}}\right)}=\frac{ n ^{2}}{2 n -1}$