A) \[\frac{8}{3}\text{ m}\]
B) \[\frac{4}{3}\text{ m}\]
C) \[\frac{3}{4}\text{ m}\]
D) \[\frac{3}{8}\text{ m}\]
Correct Answer: B
Solution :
[b] Comparing the given equation with the equation of trajectory of a projectile, \[y=x\,\,\tan \theta -\frac{\text{g}{{\text{x}}^{2}}}{2{{\text{u}}^{2}}{{\cos }^{2}}\theta },\text{ }\] we get, \[\text{tan}\theta \,\text{=}\,\,\frac{1}{\sqrt{3}}\Rightarrow \theta =30{}^\circ \] and \[2{{\text{u}}^{2}}{{\cos }^{2}}\theta =20\Rightarrow {{\text{u}}^{2}}=\frac{20}{2{{\cos }^{2}}\theta }=\frac{40}{3}\] Now, \[{{\text{R}}_{\max }}=\frac{{{\text{u}}_{2}}}{\text{g}}=\frac{40}{3\times 10}=\frac{4}{3}\text{m}\]
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