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3-2.Motion in Plane
hard
A shell fired from the base of a mountain just clears it. If $\alpha$ is the angle of projection then the angular elevation of the summit $\beta$ is
A
$\frac{1}{2} \alpha$
B
$tan^{-1}(1/2)$
C
$tan^{-1}(1/2 \,\,tan \,\, \alpha )$
D
$tan^{-1}(2 \,\,tan\,\, \alpha )$
Solution
$\tan \beta=\frac{H}{R / 2}=\frac{2 H}{R}$
$=\frac{\left(2 u^{2} \sin ^{2} \alpha\right) /(2 g)}{\left(2 u^{2} \sin \alpha \cos \alpha\right) / g}=\frac{\tan \alpha}{2}$
$\therefore \beta=\tan ^{-1}\left(\frac{\tan \alpha}{2}\right)$
Standard 11
Physics
