Physics - Kinematics Question with Solution | TestHub

We know that the range of a projectile:

$R=\frac{u^2\sin 2\theta }{g}$

Here,

$R=6+18=24$

Therefore,

$\frac{u^2\sin 2\theta }{g}=24$ ...... (i)

The equation of trajectory of a projectile is:

$y=x\tan \theta -\frac{g{x}^2}{2u^2{\cos }^2\theta }$

$3=6\tan \theta -\frac{36g}{2u^2{\cos }^2\theta }$ ...... (ii)

From equation (i),

$\frac{g}{u^2}=\frac{\sin 2\theta }{24}$

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

Substituting this in equation (ii), we get:

$3=6\tan \theta -\frac{3}{2}\tan \theta$

$3=\frac{9}{2}\tan \theta$

$\Rightarrow \theta ={\tan }^{-1}\left(\frac{2}{3}\right)$