\[(a)\;75^{\circ}\quad (b)\;15 ^{\circ} \quad (c)\;60^{\circ} \quad (d)45^{\circ}\]

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Let the base be of length 'a'

the length $AC=a/\cos \theta$

The body travels along AC. and the component of $g$ along $AC=g \sin \theta$.

using $s=ut+\large\frac{1}{2} $$at^2$

$\large\frac{a}{\cos \theta}=\frac{1}{2}$$ (g \sin \theta)t^2$

$t=\sqrt {\large\frac{2a}{g \sin \theta \cos \theta}}=\sqrt {\large\frac{4a}{g \sin 2 \theta}}$

t is minimum when $\sin 2 \theta=1$

$2 \theta=90^{\circ}\quad or \quad \theta=45^{\circ}$

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