Kinematics

JEE Main level, single correct, medium

38 of 308

Question 38 of 308

A balloon is moving up in air vertically above a point AA on the ground. When it is a height h1,{h}_{1}, a girl standing at a distance d (point B) from A (see figure) sees it at an angle 45∘45^{\circ} with respect to the vertical. When the balloon climbs up a further height h2{h}_{2}, it is seen at an angle 60∘60^{\circ} with respect to the vertical if the girl moves further by a distance 2.464d2.464d (point C). Then the height h2{h}_{2} is (given tan⁡30∘=0.5774\tan 30^{\circ}=0.5774):

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Answer: (D) dd

t45=h1d{t}_{45}=\dfrac{{h}_{1}}{d}
h1=d{h}_{1}=d .......(i)
h1+h2d+2.464d=tan⁡30∘=13=0.5774\dfrac{{h}_{1}+{h}_{2}}{d+2.464d}=\tan 30^{\circ}=\dfrac{1}{\sqrt{3}}=0.5774
h1+h2=(3.464)d×0.5774{h}_{1}+{h}_{2}=(3.464)d\times 0.5774
h1+h2=2d{h}_{1}+{h}_{2}=2d .......(ii)
∴h2=d∴{h}_{2}=d

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