A Man on a Cliff Observes a Fishing Trawler at an Angle of Depression of 30º Which is Approaching the Shore to the Point Immediately Beneath the Observer with a Uniform Speed. - Mathematics

Sum

A man on a cliff observes a fishing trawler at an angle of depression of 30º which is approaching the shore to the point immediately beneath the observer with a uniform speed. 6 minutes later, the angle of depression of the trawler is found to be 60º. Caliculate the time taken by the trawler to reach the shore

Solution

Let AB be the cliff and C and D be the two positions of th fishing trawler.

Then, ∠ACB = 30º and ∠ADB = 60º

Let AB = h.

\text{Now, }\frac{AD}{AB}=\text{cot }60^\text{o}=\frac{1}{\sqrt{3}}

\Rightarrow AD=\frac{h}{\sqrt{3}}

\text{And, }\frac{AC}{AB}=\text{cot 3}0^\text{o}=\sqrt{3}

⇒ AC = √3 h

CD=ACAD=( \sqrt{3}h-\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\Rightarrow \frac{2h}{\sqrt{3}}=6u\Rightarrowh=3\sqrt{3}u

Now,\text{ }AD=\frac{h}{\sqrt{3}}=\frac{3\sqrt{3}u}{\sqrt{3}}=3u

Time taken by trawler to reach A

=>\frac{

Concept: Heights and Distances
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