Question

The equation of trajectory of a projectile is $y=10x-\left(\frac{5}{9}\right)x^2.$ If we assume $g=10m{s}^{-2}.$ What will be the range of projectile?

• A. 36 m
• B. 24 m
• C. 18 m
• D. 9 m

Answer 1

Answer: (C)

Equation of projectile,
$y=10x-\left(\frac{5}{9}\right)x^2$
Equation of trajectory is give by
$y=x\tan \theta -\frac{g}{2u^2{\cos }^2\theta }\cdot x^2$
On comparing,
$\tan \theta =10$ and
$\frac{g}{2u^2{\cos }^2\theta }=\frac{5}{9}$
or $10u^2{\cos }^2\theta =9g$
$\therefore u^2{\cos }^2\theta =9$
Range of projectile,
$R=\frac{2u^2\sin \theta \cos \theta }{g}$
$=\frac{2u^2\tan \theta {\cos }^2\theta }{g}$
$(\because \sin \theta =\tan \theta \cos \theta )$
$=\frac{2\left(u^2{\cos }^2\theta \right)\cdot \tan \theta }{g}$
$=\frac{2\times 9\times 10}{10}=18m$