Question

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

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

Answer 1

Answer: (A)

$\frac{ h _{1}}{ d }=\tan \,45^{\circ} $
$\Rightarrow h _{1}= d\,\,$.....(1)
$\frac{ h _{1}+ h _{2}}{ d +2.464 d }=\tan 30^{\circ}$
$\Rightarrow \left(h_{1}+h_{2}\right) \times \sqrt{3}=3.46\, d$
$\left( h _{1}+ h _{2}\right)=\frac{3.46 d }{\sqrt{3}}$
$\Rightarrow d + h _{2}=\frac{3.46 d }{\sqrt{3}}$
$h _{2}= d$