Question

When a bullet is fired at a target, its velocity decreases by half after penetrating 30 cm into it. The additional thickness it will penetrate before coming to rest is

• A. 30 cm
• B. 40 cm
• C. 10 cm
• D. 50 cm

Answer 1

Answer: (C)

Let the velocity of the bullet when it strikes the target is $vcm{s}^{-1}$
After penetrating 30 cm, velocity becomes half ie.$\frac{v}{2}$
From equation $v^2=u^2+2as$
hance ${\left(\frac{v}{2}\right)}^2=v^2+2a\times 30$
or $-60a=v^2-\frac{v^2}{4}$
or $-60a=\frac{3v^2}{4}$
$a=-\frac{v^2}{80}cm{s}^{-2}$
Let the bullet further penetrates x cm before coming to rest, therefore
$v^{{}^{\prime }2}=u^{{}^{\prime }2}+2a{s}^{\prime }$
$0={\left(\frac{v}{2}\right)}^2+2\left(-\frac{v^2}{80}\right)x$ $\frac{v^{2}x}{40}=\frac{v^2}{4}$
x = 10 cm