Question

A shooter fires a bullet with a speed of $200m/s$ can just penetrate $3$ planks of equal thickness $x$. Then the number of such planks penetrated by this bullet if its velocity becomes $3$ times initial. (consider retardation is constant)

• A. $11$
• B. $15$
• C. $27$
• D. $30$

Answer 1

Answer: (C)

$v^2-u^2=2as$
$\Rightarrow 0-u^2=2\times -a\times s$
$u^2\propto s$
$\frac{{\left(u_1\right)}^2}{{\left(u_2\right)}^2}=\frac{s_1}{s_2}$
$\Rightarrow s_2={\left(\frac{u_2}{u_1}\right)}^2\times s_1$
$\Rightarrow s_2={\left(\frac{3u_1}{u_1}\right)}^2\times 3s_1$
$\therefore s_2=27s_1$