Question

In figure, the angle of inclination of the incline plane is $30°$. The horizontal velocity
$V_0$ so that the particle hits the incline plane perpendicularly is $\sqrt{\frac{xgh}{y}}$. Then value of $x\times y$ is (Where, $x\&y$ are integer and coprime.)

Answer 1

In a direction along the inclined plane,
$0=V_0\cos 30°-g\sin 30°t\Rightarrow t=\frac{\sqrt{3}{V}_0}{g}$
In a direction perpendicular to incline,
$-H\cos 30°=-V_0\sin 30°t-\frac{\left(g\cos 30°\right)t^2}{2}$
. Putting the value of t and solving, we get $V_0=\sqrt{\frac{2gH}{5}}$