question_answer

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

Correct Answer: D

Solution :

We know that distance \[(s)=\]speed\[(v)\times \]time \[(t)\] 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,   \[u=0,\,\,t=0.1\,\,s\] \[\therefore \]  \[h=\frac{1}{2}\times 10\times {{(0.1)}^{2}}=0.05\,\,m=5\,\,cm\].