  Question

# A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 metres 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∘. Find the distance travelled by the balloon during the interval.  The required distance travelled by the balloon is 18√3 m The required distance travelled by the balloon is 28√3 m The required distance travelled by the balloon is 58√3 m The required distance travelled by the balloon is 98√3 m

Solution

## The correct option is C The required distance travelled by the balloon is 58√3 m Let AB be the position of the girl and AX be the horizontal ground. Let C and D be the two positions of the balloon. Draw CL⊥AX,DM⊥AX and BN⊥DM, intersecting CL at P. Then, ∠CBP=60∘,∠DBN=30∘,AB=PL=NM=1.2 m and CL=DM=88.2 m ∴ CP = 88.2 m - 1.2 m = 87 m From right ΔBPC, we have BPCP=cot 60∘=1√3⇒BP87 m=1√3⇒BP=87 m√3 ⇒BP=87 m√3×√3√3=29√3 m From right ΔBND, we have BNDN=cot 30∘=√3⇒BP+PNCP=√3 ⇒29√3+CD87 m=√3   [∵PN=CD and DN=CP] ⇒29√3 m+CD=87√3 m ⇒CD=87√3 m−29√3 m=58√3 m Hence, the required distance travelled by the balloon is 58√3 m  Suggest corrections   