Question

The angle of elevation of a jet fighter from a point $A$ on the ground is ${60}^o$ . After a flight of $10s$ , the angle of elevation changes to ${30}^o$ . If the jet is flying at a speed of $432km/h$ . Find the constant height at which the jet is flying.

• A. $200\sqrt{3}m$
• B. $400\sqrt{3}m$
• C. $600\sqrt{3}m$
• D. $800\sqrt{3}m$

Answer 1

Answer: (C)

Since, speed of a flight be $432km/h$ .
$\therefore$ Distance cover from $A$ to $B$ ,
$d=432\times \frac{5}{18}\times 10=1200m$
Now, in $\Delta CBD$ ,
$\tan {60}^o=\frac{h}{x}\Rightarrow x=\frac{h}{\sqrt{3}}$ and in
$\Delta CAD$ , $\tan {30}^o=\frac{h}{d+x}$
$\Rightarrow$ $\frac{1}{\sqrt{3}}=\frac{h}{1200+\frac{h}{\sqrt{3}}}$
$\Rightarrow$ $1200=\sqrt{3}h-\frac{h}{\sqrt{3}}$
$\Rightarrow$ $h=600\sqrt{3}m$