Question

A shooter fires a bullet with a speed of $200 m / s$ 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)

$v^{2}-u^{2}=2 a s$
$\Rightarrow 0-u^{2}=2 \times-a \times s$
$u^{2} \propto s$
$\frac{\left(u_{1}\right)^{2}}{\left(u_{2}\right)^{2}}=\frac{s_{1}}{s_{2}}$
$\Rightarrow s_{2}=\left(\frac{u_{2}}{u_{1}}\right)^{2} \times s_{1}$
$\Rightarrow s_{2}=\left(\frac{3 u_{1}}{u_{1}}\right)^{2} \times 3 s_{1}$
$\therefore s_{2}=27 s_{1}$