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  4. An inclined plane is located at angle α =53° to the horizontal. There is a hole at point B in the inclined plane as shown in the figure. A particle is projected along the plane with speed v0 at an angle β =37° to the horizontal in such a way so that it gets into the hole. Neglect any type of friction. Find the speed v0 (in m s- 1 ) if h=1 m and l=8m . <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-g1lwnk8xj4qq.png />

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Q. An inclined plane is located at angle $\alpha =53^\circ $ to the horizontal. There is a hole at point $B$ in the inclined plane as shown in the figure. A particle is projected along the plane with speed $v_{0}$ at an angle $\beta =37^\circ $ to the horizontal in such a way so that it gets into the hole. Neglect any type of friction. Find the speed $v_{0}$ (in $m \, s^{- 1}$ ) if $h=1 \, m$ and $l=8m$ .

Question

NTA AbhyasNTA Abhyas 2020Motion in a Plane

Solution:

Solution
$h=ltan \beta - \frac{1}{2} \frac{g sin ⁡ \alpha l^{2}}{v_{0}^{2} cos^{2} ⁡ \beta }$
$v_{0}=\sqrt{\frac{g sin \alpha l^{2}}{2 \left(cos\right)^{2} ⁡ \beta \left(l tan ⁡ \beta - h\right)}}$
$=\sqrt{\frac{10 \times \frac{4}{5} \times 8 \times 8}{2 \times \frac{4}{5} \times \frac{4}{5} \left(8 \times \frac{3}{4} - 1\right)}}=9 \, ms^{- 1}$