Question

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

The Correct Option is D

We know that distance
$ \text{(sd)}\,\text{=}\,\text{speed}\,\text{(v)}\,\text{ }\!\!\times\!\!\text{ }\,\text{time}\,\text{(t)} $
$ \Rightarrow $ $ t=\frac{s}{v} $
Given, $ v=500\,m{{s}^{-1}},s=50\,m $
$ \therefore $ $ t=\frac{50}{500}=0.1\,s $
From equation of motion, for vertical displacement
$ h=ut+\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.