A hydrogen filled balloon ascending at the rate of 18 kmph was drifted by wind. Its angle of elevation at 10 and 15 minutes were found to be 60° and 45° respectively. The wind speed (in whole numbers) during the last five minutes, approximately, is equal to:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 33 km/hr
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Application |
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Given: After 10 minutes balloon will be at Point Q and after 15 minutes balloon will be at point R.
So, QS = Time × Speed = 10/60 × 18 = 3 km And RT = Time × Speed = 15/60 × 18 = 4.5 km So, RU = 4.5 – 3 = 1.5 km In triangle PQS: Tan 60 = QS/SP ⇒ √3 = 3/SP ⇒ SP = √3 In triangle PRT: Tan 45 = RT/TP ⇒ 1 = 4.5/TP ⇒ TP = 4.5 So, TS = TP – SP = (4.5 – √3) m And UQ = TS = (4.5 – √3) m Now, Wind speed = UQ/Time = (4.5 – √3)/(5/60) = (4.5 – 1.732)/(5/60) = 2.768 × 12 = 33.216 or 33 km/hr |
