Question

The equation of motion of a projectile is : $y=12x-3/4x^2$ Given that $g=10m{s}^{-2}$, what is the range of the projectile ? (in metres)

• A. $16$
• B. $12$
• C. $20$
• D. $24$

Answer 1

The correct option is A $16$

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

The general equation of a projectile motion is given by, $y=xtan\theta -\frac{g}{2u^{2}co{s}^2\theta }{x}^2$

Comparing both equation, we get $tan\theta =12$ and $\frac{g}{2u^{2}co{s}^2\theta }=\frac{3}{4}$

Now, $u^{2}co{s}^2\theta =\left(4/3\right)\left(g/2\right)=\left(4/3\right)\left(10/2\right)=40/6=20/3$

$⟹$ $ucos\theta =\sqrt{20/3}$

Also, from $tan\theta =12$

We get $\frac{\sin \theta }{cos\theta }=12$

$⟹$ $u\sin \theta =12ucos\theta =12\times \sqrt{20/3}$

Range of a projectile motion is given by, $R=\frac{u^2\sin 2\theta }{g}$

$\therefore$ $R=\frac{u^2\left(2\sin \theta cos\theta \right)}{g}=\frac{2\left(12\sqrt{20/3}\right)\left(\sqrt{20/3}\right)}{10}=\frac{20\times 24}{3\times 10}=16m$