Question

a bullet moving with a velocity of 60 m/s can just penetrate three wooden planks of equal thickness. how many such planks it can penetrate if the initial velocity is 120m/s ?​

Answer 1

Given:

A bullet moving with a velocity of 60 m/s can just penetrate three wooden planks of equal thickness.

To find:

How many such planks can be penetrated if initial velocity is 120 m/s ?

Calculation:

Let length of each plank be "L"

When initial velocity is 60 m/s :

$\therefore \: {v}^{2} = {u}^{2} + 2as$

$= > \: {(0)}^{2} = {(60)}^{2} + 2a(3L)$

$= > \: {(0)}^{2} = 3600 + 6aL$

$= > \: 0 = 3600 + 6aL$

$= > \: a = - \dfrac{3600}{6L}$

$= > \: a = - \dfrac{600}{L} \: \: \: \: ......(1)$

When initial velocity is 60 m/s:

$\therefore \: {v}^{2} = {u}^{2} + 2as$

$= > \: {(0)}^{2} = {(120)}^{2} + 2a(nL)$

$= > \: 0 = 14400 + 2a(nL)$

$= > \: 2a(nL) = - 14400$

$= > \: a(nL) = - 7200$

$= > \: \bigg \{ \dfrac{ - 600}{L} \bigg \} (nL) = - 7200$

$= > \: n = \dfrac{7200}{600}$

$= > \: n = 12$

So, the number of planks required is 12.

Hope It Helps.