Question

A man in a boat rowed away from a cliff $150$ metres high takes $2$ minutes to change the angle of elevation of the top of the cliff from ${60}^o$ to ${45}^o$. Find the speed of the boat.

Answer 1

$A/Q$, $AB=150m$

Let speed of boat= $v$ m/s

$\Rightarrow DC=2\times 60v=120v$

(Refer to Image)

In ${\Delta }^{le}ABC,\tan {60}^o=\frac{150}{x}$

$\Rightarrow x=\frac{150}{\sqrt{3}}$

In the ${\Delta }^{le}ADB,\tan {45}^o=\frac{150}{120v+x}$

$\Rightarrow 120v+x=150$

$\Rightarrow 120v+\frac{150}{\sqrt{3}}=150$

$\Rightarrow v=\frac{150}{120}[1-\frac{1}{\sqrt{3}}]$

$\Rightarrow v=0.5283$ m/s