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man from the top of a 100 metres high
tower observes a car moving towards the tower at an angle
of depression of 30°. After some time, the angle of depression
becomes 60°. The distance (in metres) travelled by the
car during this time is

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$100 \sqrt{3}$

$200 / \sqrt{3}$

$100 / \sqrt{3}$

$200 \sqrt{3}$

answer is B.

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Detailed Solution

Let $O P$ be the tower and $C 1, C 2$ be the positions
of the car (Fig. 27.13)

We have $\frac{O C_{1}}{O P} = \cot 30^{\circ} = \sqrt{3}$

$\Rightarrow O C_{1} = 100 \sqrt{3}$

Similarly $O C_{2} = 100 / \sqrt{3}$

Now $C_{1} C_{2} = O C_{1} - O C_{2}$

$\begin{array}{l} = 100 (\sqrt{3} - 1 / \sqrt{3}) \\ = 200 / \sqrt{3} \end{array}$

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