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  4. A B is an inclined plane of inclination 30° with horizontal. Point O is 20 m above point A. A particle is projected horizontally from O leftwards, and it collides with the plane A B perpendicularly. Speed of the particle at the time of projection should be (g=10 m / s 2)

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Q. $A B$ is an inclined plane of inclination $30^{\circ}$ with horizontal. Point $O$ is $20\, m$ above point $A$. A particle is projected horizontally from $O$ leftwards, and it collides with the plane $A B$ perpendicularly. Speed of the particle at the time of projection should be $\left(g=10 \,m / s ^{2}\right)$Physics Question Image

Motion in a Plane

Solution:

In $x$ direction: $v_{I}=u_{I}+a_{I} t$
$\Rightarrow 0=u \cos 30^{\circ}-g \sin 30^{\circ} t $
$\Rightarrow u \sqrt{3}=g t$ .... (i)
image
In $y$ direction: $s_{y}=u_{y} t+\frac{1}{2} a_{y} t^{2}$
$\Rightarrow 20 \cos 30^{\circ}=u \cos 60^{0} t+\frac{1}{2} g \cos 30^{\circ} t^{2}$
$\Rightarrow 20 \sqrt{3}=u t+\frac{1}{2} g t^{2} \sqrt{3}$
$\Rightarrow 20 \sqrt{3}=\frac{u^{2} \sqrt{3}}{g}+\frac{\sqrt{3}}{2} g \cdot \frac{3 u^{2}}{g^{2}} \Rightarrow 20=\frac{5 u^{2}}{2 g}$
$\Rightarrow u=\sqrt{80} m / s =4 \sqrt{5} m / s$