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A man in a boat rowing away from a cliff $150$ metres high observes that it takes $2$ minutes to change the angle of elevation of the top of the cliff from $60 °$ to $45 ° .$ The speed of the boat is

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$(1 / 2) (9 + 3 \sqrt{3}) km / h$

$(1 / 2) (9 - 3 \sqrt{3}) km / h$

$(1 / 2) (9 \sqrt{3}) km / h$

answer is A.

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Detailed Solution

$\begin{array}{l} AB = (\cot 45^{\circ} - \cot 60^{\circ}) 150 \\ = 150 (1 - \frac{1}{\sqrt{3}}) = 50 (3 - \sqrt{3}) \end{array}$

speed $= \frac{50 (3 - \sqrt{3})}{2} m /$ min.

$\begin{array}{l} = 25 (3 - \sqrt{3}) \times \frac{60}{1000} km / hr \\ = \frac{9 - 3 \sqrt{3}}{2} km / h . \end{array}$

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