question_answer

A balloon is coming down at the rate of 4 m/min. and its angle of elevation is 45o from a point on the ground which has been reduced to 30o after 10 minutes. Balloon will be on the ground at a distance of how many meters from the observer

A) \[20\,\sqrt{3}\,m\]

B) \[20\,(3+\sqrt{3})\,m\]

C) \[10\,(3+\sqrt{3})\,m\]

D) None of these

Correct Answer: B

Solution :

\[{{B}_{1}}{{B}_{2}}=h=(d\tan {{45}^{o}}-d\tan {{30}^{o}})\] Time taken = 10 min Rate =  \[4=\frac{d}{10}\left( \frac{\sqrt{3}-1}{\sqrt{3}} \right)\] \[\Rightarrow \] \[d=\frac{40\sqrt{3}}{\sqrt{3}-1}=20(3+\sqrt{3})\,m\].