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  • A projectile is given an initial velociy of , where is along the ground and is along the vertical. If g = 10m/s2 , the equation of its trajectory is :

A projectile is given  an initial velocity of (i+2j)m/s where i is along the ground and j is along the vertical. If g=10m/s2, the equation of its trajectory is?

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\\\text{The equation of projectile is given by, } \\\\ \mathrm{y}=\mathrm{x} \tan \theta-\frac{1}{2} \frac{\mathrm{g} \mathrm{x}^{2}}{\mathrm{u}^{2} \cos ^{2} \theta}$ \\\\ $\tan \theta=\frac{u_{y}}{u_{x}}=\frac{2}{1}=2$\\\\ $\therefore \mathrm{v}=2 \mathrm{x}-\frac{1}{2} \frac{10 \mathrm{x}^{2}}{\left(1^{2}+2^{2}\right) \times \frac{1}{1+\tan \theta}}=2 \mathrm{x}-\frac{1}{2} \frac{10 \mathrm{x}^{2}}{\left(1^{2}+2^{2}\right) \times \frac{1}{5}}$\\\\ $\Rightarrow y=2 x-5 x^{2}$

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