• # question_answer A projectile is given an initial velocity of $\hat{i}+2\hat{j}.$ The Cartesian equation of its path is: ($g=10\,m/{{s}^{2}}$) A) $~y=2x-5{{x}^{2}}$                    B) $~y=x-5{{x}^{2}}$C) $~4y=2x-5{{x}^{2}}$                  D) $~y=2x-25{{x}^{2}}$

$\tan \theta =\frac{u\sin \theta }{u\cos \theta }=\frac{2}{1}$ The desired equation is $y=x\tan \theta -\frac{g{{x}^{2}}}{2{{u}^{2}}{{\cos }^{2}}\theta }$of $y=2x-\frac{10{{x}^{2}}}{2{{(\sqrt{{{2}^{2}}+{{1}^{1}}})}^{2}}{{\left( \frac{1}{\sqrt{5}} \right)}^{2}}}$or $y=2x-5{{x}^{2}}$ Hence, the correction option is [a].