Question

A bullet of mass 50 g penetrates into a fixed wooden
block at speed 50 m/s. It retards uniformly and
comes to rest in 0.4 s after penetrating through half
of the thickness of the block. The thickness of the
block is

Answer 1

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

m = 50 grams.

u = 50 m/s.

v = 0 m/s.

t = 0.4 seconds.

$\huge{\bold{\underline{Explanation:-}}}$

By applying First kinematics equation.

$\large{\bold{v = u + at}}$

Substituting the values.

$\large{0 = 50 + a \times 0.4}$

$\large{a = - \frac{50}{0.4}}$

$\large{a = -125 m/s^2}$

$\huge{\boxed{\boxed{a = - 125 m/s^2}}}$

By applying Third kinematic equation.

$\large{\bold{v^2 - u^2 = 2as}}$

Substituting the values.

$\large{0 - (50)^2 = 2 \times - 125 \times S}$

$\large{ \cancel{-}2500 = \cancel{-}250 \times S}$

$\large{S = \frac{2500}{250}}$

$\large{S = 10 m}$

This 10 m is half thickness of block

For full thickness of block.

${Thickness = 2 \times S}$

$\therefore{Thickness = 2 \times 10}$

$\huge{\boxed{\boxed{Thickness = 20 m}}}$

So, the thickness of block is 20 meters.