Question

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

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

Answer 1

Answer: (D)

$1440$

Let the observing point be $O$

The height at which the plane was flying above ground is constant at $AP=QB=\sqrt{3}$ km.

In the first case, distance of projection of plane from point of observation is $\tan {60}^0=\frac{AP}{OP}⟹OP=1$ km.

In the first case, distance of projection of plane from point of observation is $\tan {30}^0=\frac{BP}{OQ}⟹OP=3$ km.

So, a distance of $3-1=2$ km. is covered in $5$ seconds. So the speed of the plane is $\frac{2\times 3600}{5}=1440$ km/hr.

So option D is the correct answer.