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 \[\text{(sd)}\,\text{=}\,\text{speed}\,\text{(v)}\,\text{ }\!\!\times\!\!\text{ }\,\text{time}\,\text{(t)}\] \[\Rightarrow \] \[t=\frac{s}{v}\] 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.