Question

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 60°. After some time, the angle of elevation reduces to 30° (see the figure given below). Find the distance travelled by the balloon during the interval.

Answer 1

Height of the girl, OO’ = 1.2 m 

∠AOB = 60° 

∠POQ = 30° 

Let OB = x m, BQ = d m, O’Q’ = y m. 

AB = PQ = Q’P – Q’Q 

= 88.2 – O’O = 88.2 – 1.2 = 87 m. 

Let OQ = ‘y’. 

Distance balloon travelled, d = BQ 

= (y – x)