The equation of motion of a projectile is $y=12x-\frac{3}{4}{x}^2$, where $x$ and $y$ are in metre. What is the range (in $\mathrm{m}$) of the projectile?

Solution

$y=\text{12}x-\frac{3}{4}{x}^2$



Range is the point where $y=0$

thus $0=\text{12}x-\frac{3}{4}{x}^2$

$\Rightarrow$    $x=0$

or   $x=\text{16}\mathrm{m}$

Hence, the correct answer is 16.