A boat is being rowed away from a cliff 150 m high. At the top of the cliff the angle of depression of the boat changes from 60o to 45o in 2 minutes. The speed of the boat is

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A boat is being rowed away from a cliff 150 m high. At the top of the cliff the angle of depression of the boat changes from 60o to 45o in 2 minutes. The speed of the boat is

Filo · Accepted Answer

Height of the lighthouse AB=150mNow,  ∠ABC=90o and ∠ACB=45o then, ∠BAC=45oNow, in right angled △ACB,⇒  tan45o=CBAB​⇒  1=CB150​⇒  CB=150m                        ------ ( 1 )In right angled △ADB,⇒  tan60o=BDAB​⇒  3​=BD150​⇒  BD=3​150​=31503​​=503​m                ----- ( 2 )Distance between CD=CB−BD                                        =(150−503​)m                                        =150−86.6m                                        =63.4mTime taken to cover 634m=2min∴  Speed of the boat =2×6063.4​=0.53m/sec                                                       =0.53×518​                                                        =1.9km/hr

Question Text	A boat is being rowed away from a cliff 150 m high. At the top of the cliff the angle of depression of the boat changes from $6 0^{o}$ to $4 5^{o}$ in 2 minutes. The speed of the boat is
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A boat is being rowed away from a cliff 150 m high. At the top of the cliff the angle of depression of the boat changes from $6 0^{o}$ to $4 5^{o}$ in 2 minutes. The speed of the boat is

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