Answer:
Given,\[\frac{{{u}^{2}}\sin 2\theta
}{g}=3\times \frac{{{u}^{2}}{{\sin }^{2}}\theta }{2g}\] or \[2\sin
\theta \cos \theta =\frac{3}{2}{{\sin }^{2}}\theta \]
or \[\tan \theta =4/3\]; so \[\sin \theta
=4/5\] and \[co\operatorname{s}\theta =3/5\]
\[\therefore \]
Horizontal range = \[\frac{{{u}^{2}}}{g}\sin 2\theta =\frac{2{{u}^{2}}}{g}\sin
\theta \cos \theta =\frac{2{{u}^{2}}}{g}\times \frac{4}{5}\times
\frac{3}{5}=\frac{24}{25}\frac{{{u}^{2}}}{g}\]
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