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 .

Question

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" /> (A) 9 (B) 3 (C) 6 (D) 12

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-g1lwnk8xmsos.png" /> h=ltan β - (1/2) (g sin â¡ α l2/v02 cos2 â¡ β ) v0=√(g sin α l2/2 (cos)2 â¡ β (l tan â¡ β - h)) =√(10 × (4/5) × 8 × 8/2 × (4)5 × (4)5 (8 × (3/4) - 1)=9 ms- 1

9

3

6

12

h=ltanβ−21​v02​cos2⁡βgsin⁡αl2​ v0​=2(cos)2⁡β(ltan⁡β−h)gsinαl2​​ =2×54​×54​(8×43​−1)10×54​×8×8​​=9ms−1

$h = lt an β - \frac{1}{2} \frac{g s in α l ^{2}}{v _{0}^{2} co s ^{2} β}$
$v_{0} = \frac{g s in α l ^{2}}{2 ( cos ) ^{2} β ( lt an β - h )}$
$= \frac{10 \times \frac{4}{5} \times 8 \times 8}{2 \times \frac{4}{5} \times \frac{4}{5} ( 8 \times \frac{3}{4} - 1 )} = 9 m s^{- 1}$