A) \[{{42}^{o}}8\]
B) \[{{53}^{o}}7\]
C) \[{{33}^{o}}7\]
D) \[{{25}^{o}}8\]
Correct Answer: B
Solution :
Let a body be projected at a velocity u at an angle \[\theta \] with the horizontal. Then horizontal range covered is given by \[R=\frac{{{u}^{2}}\sin 2\theta }{g}\] ?(i) and height H is \[H=\frac{{{u}^{2}}{{\sin }^{2}}\theta }{2g}\] ?(ii) Given, \[R=3H\] \[\therefore \] \[\frac{{{u}^{2}}\sin 2\theta }{g}=3\times \frac{{{u}^{2}}{{\sin }^{2}}\theta }{2g}\] Also, \[\sin 2\theta =2\sin \theta \cos \theta \] \[\therefore \] \[\frac{{{u}^{2}}2\sin \theta \cos \theta }{g}=3\times \frac{{{u}^{2}}{{\sin }^{2}}\theta }{2g}\] \[\Rightarrow \] \[2\cos \theta =1.5\sin \theta \] \[\Rightarrow \] \[\tan \theta =\frac{2}{1.5}=1.33\] \[\Rightarrow \] \[\theta ={{53}^{o}}7\] Hence, angle of projection is \[{{53}^{o}}7\]You need to login to perform this action.
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