Question

A rifle bullet loses 1/20^th of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is

• A. 5
• B. 10
• C. 11
• D. 20

Answer 1

Answer: (C)

11

Answer 2

Let the thickness of one plank is s if bullet enters with velocity u then it leaves with velocity

$v = \left( u - \frac { u } { 20 } \right) = \frac { 19 } { 20 } u$

from $v ^ { 2 } = u ^ { 2 } - 2 a s$

⇒ $\left( \frac { 19 } { 20 } u \right) ^ { 2 } = u ^ { 2 } - 2 a s$ ⇒ $\frac { 400 } { 39 } = \frac { u ^ { 2 } } { 2 a s }$

Now if the n planks are arranged just to stop the bullet then again from $v ^ { 2 } = u ^ { 2 } - 2 a s$

$0 = u ^ { 2 } - 2 a n s$

⇒ $n = \frac { u ^ { 2 } } { 2 a s } = \frac { 400 } { 39 }$

⇒ $n = 10.25$

As the planks are more than 10 so we can consider n = 11