Question

A rifle shoots a bullet with a muzzle velocity of $500m{s}^{-1}$ at a small target $50m$ away. To hit the target the rifle must be aimed: (Take $g=10m{s}^{-2}$ )

• A. exactly at the target
• B. 10 cm below the target
• C. 10 cm above the target
• D. 5 cm above the target

Answer 1

Answer: (D)

We know that distance
$(sd)=\mathrm{speed}(v)\times \text{ time }(t)$
$\Rightarrow t=\frac{s}{v}$
Given, $v=500m{s}^{-1},s=50m$
$\therefore t=\frac{50}{500}=0.1s$
From equation of motion, for vertical displacement
$h=ut+\frac{1}{2}g{t}^2$
Given, $u=0,t=0.1s$
$\therefore h=\frac{1}{2}\times 10\times (0.1{)}^2$
$=0.05m=5cm$.
Hence, the rifle must be aimed $5cm$ above the target.