Question

A bullet is moving with 10ms hits a wooden plank. The bullet is stopped when it penetrates the plank 2cm deep. Calculate the retardation of the bullet

Answer 1

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$\underline{\underline{\huge{\textbf{Solution:}}}}$

Given,
Initial Velocity of the Bullet $u = 10\: m/s$

Distance penentrated into the wooden block by the bullet after hitting $s = 2\: cm$

Then the Bullet is stopped.

$\underline{\large{\textsf{step-1:}}}$
Express the distance penentrated by the bullet in m

We have,
$\bigstar 1\: m = 100\: cm$

$\implies 1\: cm = \frac{1}{100}\: m$

Multiply 2 on Both Sides

$\implies 2\: cm = \frac{2}{100}\: m = 0.02\: m$

$\therefore$ Distance penentrated into the wooden block by the bullet after hitting $s = 0.02\: m$

$\underline{\large{\textsf{step-2:}}}$
Note the Final Velocity of the Bullet

As the Bullet is stopped,
Final Velocity of the bullet $v = 0\: m/s$

$\underline{\large{\textsf{step-3:}}}$
Find the Acceleration possessed by the Bullet.

Using the Equation of Motion,
$\bigstar v^{2}-u^{2}= 2as$

Let acceleration of Bullet be $a\: m/s$

Substituting Values

$\implies (0)^{2}-(10)^{2}= 2 \times a \times 0.02$

$\implies -(100) = 2 \times a \times 0.02$

$\implies a = \dfrac{-100}{0.04}$

$\implies a =-2500\: m/s^{2}$

This is the Negative Acceleration (or Retardation) of Bullet.

Here,
Negative sign just indicates the fact that Velocity of the bullet is decreasing as it penetrates into the wooden block and finally becomes zero, when it penetrates 2cm inside the wooden block.

$\therefore$
Retardation of the Bullet is $\underline{2500\: m/s^{2}}$

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Answer 2

Intial Velocity of Bullet (u)=10 m/s
Final Velocity After Penetrating wood(v)=0 m/s
Given Distance Travel(s) =2cm
Distance (s)=0.02 METRES

What Is Retardation
It simply means Accerlation Needed to come at rest.It is Denoted As -

Let Retardation=r

Use Newton Equation of Motion..
V²=U²+2rs

Given,
0²=10²+2×r×0.02

Now
0²=10²+2×r×0.02
0=100+0.04r
0.04r=0-100
0.04r=-100
R=-100÷0.04
R=-2500 m/s²

Why We take - because Retardation is in Minus .

Retardation=-2500 m/s²