Question

A bullet fired from a rifle loses 20% of its speed while passing through a wooden plank then minimum number of wooden planks repaired to completely stop the bullet is

Answer 1

https://www.quora.com/A-bullet-loses-1-20th-of-its-velocity-when-passing-through-a-plank-What-is-the...   

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Answer 2

The number of wooden planks required to just stop the bullet is 3

Explanation:

Bullet looses 20% of its speed while passing through the wooden 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

$v=u-u-0.2u$

$\implies v=0.8u$

Therefore,

$(0.8u)^2=u^2-2ad$

$\implies 2ad=u^2[1-0.64]$

$\implies 2ad=u^2[0.36]$

$\implies 2ad=0.36u^2$  .............. (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)

$\frac{1}{N}=0.36$

$\implies N=\frac{1}{0.36}$

$\implies N=\frac{100}{36}=2.78$

But N must be a natural number

Therefore, N=3

Hope this answer is helpful.

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