A) possible to hit a target 5 km away
B) not possible to hit a target 5 km away
C) prediction is not possible
D) none of the above
Correct Answer: B
Solution :
Key Idea: It is not possible to hit beyond maximum range. The body covers a horizontal distance AB during its flight. This horizontal range is given by \[R=\frac{{{u}^{2}}\sin 2\theta }{g}\] ?(i) where, u is velocity of projection, \[\theta \] is angle of projection and g is acceleration due to gravity. For maximum horizontal range \[\sin 2\theta =1\] \[\therefore \] \[R{{}_{\max }}=\frac{{{u}^{2}}}{g}\] ?(ii) Given, \[R=3km,\theta ={{30}^{o}}\] \[\therefore \]From Eq. (i) \[\frac{{{u}^{2}}}{g}=\frac{R}{\sin 2\theta }=\frac{3}{\sin {{60}^{o}}}=\frac{3\times 2}{\sqrt{3}}=\sqrt{3}\times 2\] \[\frac{{{u}^{2}}}{g}=3.464\,m\] Hence, maximum range with velocity of projection u cannot be more than 3.464m. Hence, it is not possible to hit a target 5 km away.You need to login to perform this action.
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