Q. A rifle shoots a bullet with a muzzle velocity of $ 500\,ms^{-1} $ at a small target $50\, m$ away. To hit the target the rifle must be aimed: (Take $ g=10\,ms^{-2} $ )
Jharkhand CECEJharkhand CECE 2005
Solution:
We know that distance
$( sd )=\operatorname{speed}( v ) \times \text { time }( t ) $
$\Rightarrow t=\frac{s}{v}$
Given, $v=500\, ms ^{-1}, s=50\, m$
$\therefore t=\frac{50}{500}=0.1\, s$
From equation of motion, for vertical displacement
$h=u t+\frac{1}{2} g t^{2}$
Given, $u=0, t=0.1 s$
$\therefore h=\frac{1}{2} \times 10 \times(0.1)^{2}$
$=0.05 \,m=5 \,cm$.
Hence, the rifle must be aimed $5\, cm$ above the target.
