A particle is projected with a certain velocity at an angle $\mathrm{\alpha }$ above the horizontal from the foot of an inclined plane of inclination 30°. If the particle strikes the plane normally, then $\mathrm{\alpha }$ is equal to

${\mathrm{t}}_{\mathrm{AB}}=\text{ time of flight of projectile }=\frac{2\mathrm{usin}\left(\mathrm{\alpha }-30°\right)}{\mathrm{gcos}30°}$

$\mathrm{Now} \mathrm{component} \mathrm{of} \mathrm{velocity} \mathrm{along} \mathrm{the} \mathrm{plane} \mathrm{becomes} \mathrm{zero} \mathrm{at} \mathrm{point} \mathrm{B}:$ 

$0=ucos\left(\alpha -30°\right)-\mathrm{gsin}30°\times \mathrm{T}$

$\Rightarrow \mathrm{ucos}\left(\mathrm{\alpha }-30°\right)=\mathrm{gsin}30°\times \frac{2u\sin \left(\mathrm{\alpha }-30°\right)}{\mathrm{gcos}30°}$

$\Rightarrow \tan \left(\mathrm{\alpha }-30°\right)=\frac{\cot 30°}{2}=\frac{\sqrt{3}}{2}$

$\Rightarrow \mathrm{\alpha }=30°+{\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$