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 $2.464d$ (point $C)$ Then the height $h_2$ is (given $\tan 30^{\circ }=0.5774)$ :

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

Answer 1

Answer: (A)

$\frac{h_1}{d}=\tan 45^{\circ }$
$\Rightarrow h_1=d$.....(1)
$\frac{h_1+h_2}{d+2.464d}=\tan 30^{\circ }$
$\Rightarrow \left(h_1+h_2\right)\times \sqrt{3}=3.46d$
$\left(h_1+h_2\right)=\frac{3.46d}{\sqrt{3}}$
$\Rightarrow d+h_2=\frac{3.46d}{\sqrt{3}}$
$h_2=d$