Question

An aeroplane flying horizontally 1000√3 m above the ground is observed at an angie of elevation 60° from a point on the ground after 10 seconds ,the angle of elevation at the point observation to 30° . Find the speed of the plane in m/s.

Answer 1

Speed is 200m/s

Refer the attachment.

Answer 2

Answer:

The speed of the plane is 200 m/s.

Step-by-step explanation:

Given : An Aeroplane flying horizontally 1000√3 m above the ground is observed at an angle of elevation 60° from a point on the ground after 10 seconds ,the angle of elevation at the point observation to 30°.

To find : The speed of the plane in m/s.

Solution :

Refer the attached figure.

Let AB=y,BC=x

According to figure,

$\tan 30^\circ=\frac{DC}{AC}$

$\frac{1}{\sqrt3}=\frac{1000\sqrt3}{x+y}$

$x+y=3000$ ....[1]

$\tan 60^\circ=\frac{BE}{AB}$

$\frac{1}{\sqrt3}=\frac{1000\sqrt3}{y}$

$y=1000$ ....[2]

Put [2] in [1],

$x+y=3000$

$x+1000=3000$

$x=2000$

Distance = 2000 m

Time taken = 10 seconds

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

$\text{Speed}=\frac{2000}{10}$

$\text{Speed}=200m/s$

Therefore, The speed of the plane is 200 m/s.