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A boat is being rowed away from a cliff $150$ m high. From the top of the cliff, the angle of depression of the boat changes from $60^{o}$ to $45^{o}$ in 1 minute. If $\sqrt{3} = 1.73$ , then what is the speed of the boat?

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4.31

km/hr

3.81

km/hr

4.63

km/hr

3.91

km/hr

answer is B.

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Detailed Solution

It is given that a boat is being rowed away from a cliff

150

m high.
From the top of the cliff, the angle of depression of the boat changes from

60^{o}

45^{o}

in 1 minute.
Let AB be the cliff and C and D be the two positions of the boat. Then,

AB = 150

∠ ACB = 60^{o}

and

∠ ADB = 45^{o}

Now, in △BAD,

\cot 45^{o}

\frac{AD}{AB}

⇒

1 = \frac{AD}{150}

AD = 150

m
In △ BAC,

\cot 60^{o}

\frac{AC}{AB}

⇒

\frac{1}{\sqrt{3}} = \frac{AC}{150}

⇒

AC = \frac{150}{\sqrt{3}}

m
⇒ AC =

\frac{150 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}

⇒ AC = 50

\sqrt{3}

⇒ AC = 50 x 1.73
⇒ AC = 86.5 m
⇒

CD = AD - AC

⇒

CD = (150 - 86.5)

⇒

CD = 63.5

m
⇒ Speed of the boat =

\frac{63.5}{60}

m/s.
⇒ Speed of the boat =

(\frac{63.5}{60} \times \frac{18}{5})

km/hr.
⇒ Speed of the boat =

3.81

km/hr.
Hence, the correct option is 2.

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A boat is being rowed away from a cliff 150 m high. From the top of the cliff, the angle of depression of the boat changes from 60o to 45o in 1 minute. If 3=1.73, then what is the speed of the boat?

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A boat is being rowed away from a cliff $150$ m high. From the top of the cliff, the angle of depression of the boat changes from $60^{o}$ to $45^{o}$ in 1 minute. If $\sqrt{3} = 1.73$ , then what is the speed of the boat?