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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 ?

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

$H=\large\frac{u^2 \sin ^2 \alpha}{2g}$=Greatest height
$R=\large\frac{u^2 \sin 2 \alpha}{g}$ =Horizontal range
$H=R$
$\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.
edited May 23, 2014

+1 vote