Question

A $10g$ bullet is fired at a plank of wood with a speed of $200m{s}^{-1}$. After passing through the plank, which is $1m$ thick, the speed of the bullet reduces to $100m{s}^{-1}$. Find the average resistance offered by the plank.

Answer 1

Step 1: Given Data:

Initial velocity $u=200m{s}^{-1}$

Final velocity $v=100m{s}^{-1}$

The thickness of the plank $S=1m$

Mass of the bullet $m=10g=0.01kg$

Step 2: Calculate the Retardation

According to the third equation of motion

$v^2=u^2+2\left(-a\right)S$

where $-a$ is the retardation of the bullet.

Upon substituting the values we get,

${100}^2={200}^2+2\times 1\times \left(-a\right)$

$\Rightarrow 2a={200}^2-{100}^2$

$\Rightarrow 2a=\left(200+100\right)\left(200-100\right)$

$\Rightarrow 2a=300\times 100$

$\Rightarrow 2a=3\times {10}^4$

$\Rightarrow a=1.5\times {10}^{4}m{s}^{-2}$

Step 3: Calculate the Average Resistance

So average resistance offered

$F=ma$

Upon substituting the values we get,

$F=0.01\times 1.5\times {10}^4$

$=150N$

Hence, the average resistance offered by the plank is $150N$.