Question

An aeroplane flying at a constant speed, parallel to the horizontal ground, $\sqrt{3}km$ above it, is observed at an elevation of ${60}^{\circ }$ from a point on the ground. If, after five seconds, its elevation from the same point, is ${30}^{\circ }$, then the speed (in $km/hr$) of the aeroplane, is :

• A. $1500$
• B. $1440$
• C. $750$
• D. $720$

Answer 1

The correct option is B $1440$


Let the speed of the plane be $skm/hr$,
We know that,
$\tan {30}^{\circ }=\frac{BE}{CE}\Rightarrow CE=3km\tan {60}^{\circ }=\frac{AD}{CD}=\frac{BE}{CD}\Rightarrow CD=1km$
Now,
$DE=CE-CD=2km=AB$
So,
$s\times \frac{5}{3600}=2\Rightarrow s=1440km/hr$