(Q1) A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60o. After sometime, the angle of elevation reduces to 30o. Find the distance travelled by the balloon during the interval.

Answer :

3060xdd88.2m88.2 - 1.2 = 87m

Height of the balloon from the ground = 88.2 m

Height of the girl = 1.2 m

Angles of elevations = 60° and 30°

Let the distance travelled = d m

tan 60° =
x
√ =
x

= √ x ....(1)

x =
√
Also tan 30° =
x + d
1
√
 =
x + d
=
x + d
√
 ....(2)

From equations (1) and (2)

√ x =
x + d
√

√ × √ x = x + d

x = x + d

x = d

Distance travelled = ×
√
 = ×
× √3 × √3
√
 = √3 m