Question

A man on cliff observes fishing trawler at an angle of depression of 30° which is approaching the share point. 6 minutes later, the angle of depression of the trawler is found to be 60°. Find the time taken by trawler to reach the foot of the cliff.



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Answer 1

Let AB be the cliff and C and D be the two positions of the fishing trawler.
Then, ∠ACB = 30º and ∠ADB = 60º

Let AB = h.
Now,
$\frac{ad}{ab} = \cot(60) = \frac{1}{ \sqrt{3} }$
$= > ad = \frac{h}{ \sqrt{3} }$
And,
$\frac{ac}{ab} = \cot(30) = \sqrt{3}$
$= > ac = \sqrt{3} h$
$cd = ac - ad = ( \sqrt{3h} - \frac{h}{ \sqrt{3} } ) = \frac{2h}{ \sqrt{3} }$
Let u m/min be the uniform speed of the trawler.
Distance covered in 6 min = 6u metres.
Therefore,
$cd = 6u = > \frac{2h}{ \sqrt{3} } = 6u = > h = 3 \sqrt{3} \: u$
Now,
$ad = \frac{h}{ \sqrt{3} } = \frac{3 \sqrt{3} u}{ \sqrt{3} } = 3u$
Time taken by trawler to reach A
$= \frac{distance \: ad}{speed} \: = a \: = \frac{3u}{u} = 3 \: min.$

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