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, 9 is angle of projection and g is acceleration due to gravity. For maximum horizontal range \[\sin \,2=1\] \[\therefore \] \[{{R}_{\max }}=\frac{{{u}^{2}}}{g}\] ?. (ii) Given, \[R=3\,km,\,\theta ={{30}^{o}}\] \[\therefore \] From Eq. (i) \[\frac{{{u}^{2}}}{g}=\frac{R}{\sin \,2\theta }=\frac{3}{\sin \,{{60}^{o}}}=\frac{3\times 2}{\sqrt{3}}=\sqrt{3}\times 2\] \[\therefore \] \[\frac{{{u}^{2}}}{g}=3.464\,\,m\] Hence, maximum range with velocity of projection u cannot be more than 3.464 m. Hence, it is not possible to hit a target 5 km away.You need to login to perform this action.
You will be redirected in
3 sec