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QJEEM20Ph683d: JEE Main 2020 Physics - Class 11 JEEM20Ph683d Solution: A balloon is moving up in air vertically above a point A on the …

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 distanced (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) JEE Main 2020 (Online) 5th September Morning Slot Physics - Motion in a Plane Question 55 English

Multiple Choice Options

  • A 0.464d
  • B d
  • C 0.732d
  • D 1.464d

Step-by-Step Verified Solution

JEE Main 2020 (Online) 5th September Morning Slot Physics - Motion in a Plane Question 55 English Explanation

From ΔABD\Delta ABD

tan⁡45=h1d\tan 45 = {{{h_1}} \over d}

⇒1=h1d\Rightarrow 1 = {{{h_1}} \over d}

⇒h1=d\Rightarrow {h_1} = d

From ΔACE\Delta ACE

tan⁡30=h1+h2d+2.464d\tan 30 = {{{h_1} + {h_2}} \over {d + 2.464d}}

⇒\Rightarrow 0.5774=d+h23.464d0.5774 = {{d + {h_2}} \over {3.464d}}

⇒\Rightarrow d+h2=0.5774×3.464×dd + {h_2} = 0.5774 \times 3.464 \times d

⇒\Rightarrow h2=2.0001136d−d{h_2} = 2.0001136d - d

⇒\Rightarrow h2=2.000d−d=d{h_2} = 2.000d - d = d

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