Question

A projectile is given an initial velocity $\hat{i}+2\hat{j}$. The Cartesian equation of its path is ($g=10m{s}^{-}2$)

• A. $y=2x-5x^2$
• B. $9y=12x-5x^2$
• C. $y=0x-5x^2$
• D. $5y=x-9x^2$

Answer 1

The correct option is A $y=2x-5x^2$

The equation of projectile is given by

$y=xtan\theta -\frac{1}{2}\frac{g{x}^2}{u^{2}co{s}^2\theta }$

Here,

$tan\theta =\frac{U_y}{U_x}=\frac{2}{1}=2$

Therefore,

$y=2x-\frac{1}{2}\frac{10x^2}{(1^2+2^2)\times \frac{1}{1+tan\theta }}=2x-\frac{1}{2}\frac{10x^2}{(1^2+2^2)\times \frac{1}{5}}$

$⟹y=2x-5x^2$