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Vishesh Gupta

· started a discussion

· 1 Months ago

doubt (Question:97622.0)

it should be east and west not north and south.

Question:
A boy standing in the middle of a field, observes a flying bird in the north at an angle of elevation of 30° and after 2 minutes, he observes the same bird in the south at an angle of elevation of 60°. If the bird flies all along in a straight line at a height of 50\(\sqrt[]{3}\) m, then its speed in km/h is:
Options:
A) 4.5
B) 3
C) 9
D) 6
Solution:

AB = CD = 50\(\sqrt[]{3}\) meter

From ∆ OAB,

tan 30° = AB/OA

\(\Rightarrow \cfrac{1}{\sqrt[]{3}}=\cfrac{50\sqrt[]{3}}{OA}\)

⇒ OA = 50\(\sqrt[]{3}\) × \(\sqrt[]{3}\) = 150 meter

From ∆ OCD,

tan 60° = \(\cfrac{CD}{OC}\)

\(\Rightarrow \sqrt[]{3}=\cfrac{50\sqrt[]{3}}{OC}⇒ OC = 50 \) meter

∴ BD = AC = 150 + 50 = 200 meter

∴ Speed of bird = \(\cfrac{200}{2}\) = 100m/minute

= \(\cfrac{100}{1000}\) × 60 kmph = 6 kmph

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