A balloon is moving up in air vertically above a point A on the ground . When it is at height h1…..

Q: A balloon is moving up in air vertically above a point A on the ground . When it is at height h1 , a girl standing at a distance d as shown in figure . sees it at an angle 45° with respect to vertical . When the balloon climbs up a further height h2 , it is seen at an angle 60° with respect to vertical if the girl moves further by a distance 2.464 d . Then height h2 is (given tan30° = 0.5774)

Numerical

(a) 1.464 d

(b) 0.732 d

(c) 0.464 d

(d) d

Ans: (d)

Sol:From figure , $\large \frac{h_1}{d} = tan45^o $

$\large \frac{h_1}{d} = 1 $

h1 = d

$\large \frac{h_1+h_2}{d+2.464 d} = tan30^o $

$\large \frac{h_1+h_2}{d+2.464 d} = 0.5744 $

h1 + h2 = 2 d

h2 = d