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 a height ${h}_{1},$ a girl standing at a distance d (point B) from A (see figure) sees it at an angle $45 °$ with respect to the vertical. When the balloon climbs up a further height ${h}_{2}$ , it is seen at an angle $60 °$ with respect to the vertical if the girl moves further by a distance $2 . 464d$ (point C). Then the height ${h}_{2}$ is (given $\tan 30 ° = 0 . 5774$ ):

A balloon is moving up in air vertically above a point A on the ground. When it is a height h _ 1 , a girl standing at

Options

A $1 . 464d$
B $0 . 732d$
C $0 .464 d$
D $d$

Correct answer

D. $d$

Step-by-step solution

${t}_{45} = \dfrac{{h}_{1}}{d}$

${h}_{1} = d$ .......(i)

$\dfrac{{h}_{1} + {h}_{2}}{d + 2 . 464d} = \tan 30 ° = \dfrac{1}{\sqrt{3}} = 0 . 5774$

${h}_{1} + {h}_{2} = ( 3 . 464 ) d \times 0 . 5774$

${h}_{1} + {h}_{2} = 2d$ .......(ii)

$∴ {h}_{2} = d$

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