question_answer

A bullet is fired at a target with a velocity 80 m/s and penetrates 50 cm into it. If this bullet were fired into a target 25 cm thick with equal velocity, with what velocity would it emerge, supposing the resistance to be uniform and the same in both the cases?

A)  \[\sqrt{80}m/s\]             

B)         \[\frac{40}{\sqrt{2}}m/s\]

C)  \[40m/s\]          

D)         \[40\sqrt{2}m/s\]  

Correct Answer: D

Solution :

  For first case, \[{{v}^{2}}={{u}^{2}}+2as\] \[\therefore \]  \[0=(80)2+2\times 9\times 0.5\] \[\Rightarrow \]               \[a=-6400\,\,m/{{s}^{2}}\] For second case,\[{{v}_{1}}^{2}={{u}^{2}}+2a{{s}_{1}}\]                    \[={{(80)}^{2}}-2\times 6400\times \frac{1}{4}\]                    \[=6400-3200=3200\] \[\therefore \]        \[{{v}_{1}}=\mathbf{40}\sqrt{\mathbf{2}}\]