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At what departure angle should a body be projected so that the maximum vertical height attained by a projectile is equal to the horizontal range ?

\[(a)\;\alpha=\tan ^{-1} 1/4 \quad (b)\;\alpha=\tan ^{-1} 1/2 \quad (c)\;\alpha=\tan ^{-1} 2 \quad (d)\;\alpha=\tan ^{-1} 4\]

1 Answer

$H=\large\frac{u^2 \sin ^2 \alpha}{2g}$=Greatest height
$R=\large\frac{u^2 \sin 2 \alpha}{g}$ =Horizontal range
$\quad=>\large\frac{\sin \alpha}{2}$$=2 \sin \alpha \cos \alpha $
$\quad=>\large\frac{\sin \alpha}{\cos \alpha}$$=4=> \tan \alpha=4$
$\quad=>\tan \alpha=4$
$\quad=>\alpha=\tan ^{-1}4$
Hence d is the correct answer. 
answered Jun 20, 2013 by meena.p
edited May 23, 2014 by lmohan717

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