Question

An aeroplane is flying at a speed of 120m/s. A boy watches the plane move from that instant when it was above his head to an instant after 6 seconds from initial instant. The angle of inclination after 6 seconds is ${30}^{\circ }$. Which of the following is/are correct?

• A. The height at which the aeroplane is flying is 1247m.
• B. The height at which the plane is flying is 1200m.
• C. The distance covered by the plane is 720m.
• D. None of the above.

Answer 1

Answer: (A), (C)

The correct options are
A

The height at which the aeroplane is flying is 1247m.

C

The distance covered by the plane is 720m.

The scenario can be represented with the following image

Here,

A is the position of the boy

B is the initial position of the aeroplane

C is the final position of the aeroplane

Distance covered by aeroplane in 6 sec = 120m/s x 6sec = 720m

Since the angle of inclination is ${30}^{\circ }$,

$\Rightarrow \tan {30}^{\circ }=\frac{BC}{AB}$

$\Rightarrow \frac{1}{\left(\sqrt{3}\right)}=\frac{BC}{AB}$

$\Rightarrow AB=720\sqrt{3}$

$\Rightarrow AB=1247m$