Question : A hydrogen-filled balloon ascending at the rate of 18 km/hr drifted by the wind. Its angle of elevation at the 10th and 15th minutes were found to be 60° and 45°, respectively. The wind speed (in whole numbers) during the last five minutes, approximately, is equal to:
Option 1: 7 km/hr
Option 2: 11 km/hr
Option 3: 26 km/hr
Option 4: 33 km/hr
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Correct Answer: 33 km/hr
Solution :
Given: A hydrogen-filled balloon ascending at the rate of 18 km/hr drifted by the wind. Its angle of elevation at the 10th and 15th minutes were found to be 60° and 45°, respectively.
We know the formula, $\text{speed}=\frac{\text{distance}}{\text{time}}$.
Since, BD = time × speed (Since the balloon reaches B at the 10
th
minute)
$⇒BD=\frac{10}{60}\times18=3$ km
Since, CE = time × speed.
$⇒CE=\frac{15}{60}\times18=4.5$ km (Since the balloon reaches C at the 10
th
minute)
CF = CE – BD = $4.5-3=1.5$ km
In $\triangle BDA$,
$\tan\ 60°=\frac{BD}{AD}$
$⇒\sqrt{3}=\frac{3}{AD}$
$⇒AD=\sqrt3$
In $\triangle CAE$,
$\tan\ 45°=\frac{CE}{AE}$.
$⇒1=\frac{4.5}{AE}$
$⇒AE=4.5$
So, DE = AE – AD $=4.5-\sqrt3$
Also, DE = BF
So, its speed is given as, $\frac{4.5–\sqrt3}{\frac{5}{60}}=\frac{(4.5–1.732)\times60}{5}=\frac{2.768}{5}\times60 = 33$ km/hr
Hence, the correct answer is 33 km/hr.
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