Question

A man in a boat rowed away from a cliff $50$ m high It takes $2$ minutes to change the elevation at the top of the cliff from ${60}^{\circ }$ to ${45}^{\circ }$ The speed of the boat is

• A. $\frac{9-3\sqrt{3}}{2}km/h$
• B. $\frac{9+3\sqrt{2}}{2}km/h$
• C. $\frac{9\sqrt{3}}{2}km/h$
• D. $9\sqrt{3}km/h$

Answer 1

The correct option is A $\frac{9-3\sqrt{3}}{2}km/h$

$\tan {60}^{\circ }=\frac{150}{y}$ or $\sqrt{3}=\frac{150}{y}$
$\therefore y=\frac{150}{\sqrt{3}}$
$\tan {45}^{\circ }=\frac{150}{x+y}$ or $x+y=150$
$\therefore x=150-\frac{150}{\sqrt{3}}$
Distance travelled in $2$ min=$150-\frac{150}{\sqrt{3}}m$
$\therefore$Speed=$\frac{150\sqrt{3}-150}{\sqrt{3}}\times 30$
=$\frac{150(\sqrt{3}-1)\times 30}{1000\sqrt{3}}$ km/h
=$\frac{9-3\sqrt{3}}{2}$ km/h