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A projectile aimed at a mark which is in the horizontal plane through the point of projection falls \( a \mathrm{~cm} \) short of it when the elevation is \( \alpha \) and goes \( b \mathrm{~cm} \) too far when the elevation is \( \beta \). Show that if the velocily of projection is same in all the cases, the proper elevation is
\[
\frac{1}{2} \sin ^{-1}\left(\frac{b \sin 2 \alpha+a \sin 2 \beta}{a+b}\right)
\]
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