Question

A bullet moving with a velocity of 200 m/s strikes a wooden block and pierces up to 10 cm into it. Calculate the magnitude of retardation of the bullet, while piercing the wooden block, assuming the retardation to be uniform. What time is taken by the bullet piercing through the wooden block?

Answer 1

Given

Initial velocity, $u=200m/s$.

Final velocity, $v=0m/s$. (Bullet comes to rest)

The thickness of wood pierced, $s=10cm=0.1m$.

Calculation of retardation

Using the third equation of motion,

$v^2=u^2+2as$

$a=\frac{v^2-u^2}{2s}$

$a=\frac{{\left(0\right)}^2-{\left(200\right)}^2}{2\times 0.1}=\frac{-40000}{0.2}=-200000m/s^2.$ (Negative sign indicates retardation)

Hence, the magnitude of retardation of the bullet is 200000 m/s².

Calculation of time

Using the first equation of motion,

$v=u+at$.

$0=200-200000t$

$t=\frac{200}{200000}=1\times {10}^{-3}s.$

Hence, the time is taken by the bullet piercing through the wooden block is $\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathit{s}\mathbf{.}$