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3-2.Motion in Plane
hard
A ball is thrown from the ground to clear a wall $3\,m$ high at a distance of $6\,m$ and falls $18\,m$ away from the wall, the angle of projection of ball is
A
$\tan ^{-1}\left(\frac{3}{2}\right)$
B
$\tan ^{-1}\left(\frac{2}{3}\right)$
C
$\tan ^{-1}\left(\frac{1}{2}\right)$
D
$\tan ^{-1}\left(\frac{3}{4}\right)$
Solution
(b)
$R=\frac{u^2 \sin 2 \theta}{g}=24………(i)$
In $y=x \tan \theta-\frac{g x^2}{2 u^2 \cos ^2 \theta}$
$3=6 \tan \theta-\frac{36 g}{2 u^2 \cos ^2 \theta}………..(ii)$
From Eq.$(i)$, $\quad \frac{g}{u^2}=\frac{\sin 2 \theta}{24}=\frac{\sin \theta \cos \theta}{12}$
Substituting in Eq.$(ii)$, we have
$3=6 \tan \theta-\frac{3}{2} \tan \theta=\frac{9}{2} \tan \theta$
$\therefore \theta=\tan ^{-1}\left(\frac{2}{3}\right)$
Standard 11
Physics
