A balloon is moving up in air vertically above a point A on the… | JEE Main 2020 (5 Sep, Shift 1)

Q9JEE Main 2020 · 5 SEP · SHIFT 1Medium

Motion in a Plane (2-D Kinematics)

A balloon is moving up in air vertically above a point A on the ground. When it is at a height h1, a girl standing at a distance d (point B) from A (see figure) sees it at an angle 45o with respect to the vertical. When the balloon climbs up a further height h2, it is seen at an angle 60o with respect to the vertical if the girl moves further by a distance 2.464 d (point C). Then the height h2 is (given tan 30o = 0.5774)

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Answer: (b)

At B (45 $^\circ$ with vertical): $\tan45^\circ = \frac{d}{h_1} \Rightarrow h_1 = d$
At C (60 $^\circ$ with vertical): $\tan60^\circ = \frac{d + 2.464d}{h_1 + h_2} = \frac{3.464d}{h_1 + h_2}$
$h_1 + h_2 = \frac{3.464d}{1.732} = 2d \Rightarrow h_2 = d$
So the answer is (b) $d$ .

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Motion in a Plane (2-D Kinematics) question from JEE Main 2020 (5 Sep, Shift 1)

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