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Q.
The equation of trajectory of a projectile is $y=10 x-\left(\frac{5}{9}\right) x^{2} .$ If we assume $g=10 m s^{-2} .$ What will be the range of projectile?
Motion in a Plane
Solution:
Equation of projectile,
$y=10 x-\left(\frac{5}{9}\right) x^{2}$
Equation of trajectory is give by
$y=x \tan \theta-\frac{g}{2 u^{2} \cos ^{2} \theta} \cdot x^{2}$
On comparing,
$\tan \theta=10$ and
$\frac{g}{2 u^{2} \cos ^{2} \theta}=\frac{5}{9}$
or $10 u ^{2} \cos ^{2} \theta=9 g$
$\therefore u^{2} \cos ^{2} \theta=9$
Range of projectile,
$R =\frac{2 u ^{2} \sin \theta \cos \theta}{ g }$
$=\frac{2 u ^{2} \tan \theta \cos ^{2} \theta}{ g }$
$(\because \sin \theta=\tan \theta \cos \theta)$
$=\frac{2\left( u ^{2} \cos ^{2} \theta\right) \cdot \tan \theta}{ g }$
$=\frac{2 \times 9 \times 10}{10}=18\, m$