Question

A rifle bullet loses 1/20th of its velocity in passing through a plank. the least no. of such planks needed to just stop the bullet is?

a)5 b)10, c)11 d)20

Answer 1

d is the right answers

Answer 2

The least number of planks required to just stop the bullet is 11

Therefore option (c) is correct.

Explanation:

Bullet looses 1/20th of its velocity while passing through plank

Let the resistance offered by the plank be a

if the initial velocity of bullet be u and final velocity be v and the depth of plank d

Then

By the second equation of motion

$v^2=u^2-2as$

$v^2=u^2-2ad$

But

$v=u-\frac{1}{n}u$

$\implies v=u(1-\frac{1}{20})=\frac{19u}{20}$

Therefore,

$u^2(\frac{19u}{20})^2=u^2-2ad$

$\implies 2ad=u^2[1-(\frac{19}{20})^2]$

$\implies 2ad=u^2[1-\frac{361}{400}]$

$\implies 2ad=u^2[\frac{39}{400}]$  .............. (1)

Let there are N planks

Then, after passing through these N planks, the velocity of bullet will be zero

Thus,

$0^2=u^2-2aNd$

$\implies 2aNd=u^2$  ................... (2)

Dividing eq (1) by eq (2)

$\frac{1}{N}=\frac{39}{400}$

$\implies N=\frac{400}{39}=10.25$

But the no. of planks must be whole number

Therefore, N = 11

Hope this answer is helpful.

Know More:

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