# An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60°. After 10 seconds, its elevation is observed to be 30°. Find the speed of the aeroplane in km / hr.

Given: An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60°. After 10 seconds, its elevation is observed to be 30°.

To find: the speed of the aeroplane in km / hr.

Solution:

Draw the figure according to given information

In the fig

let C be the initial position of the aeroplane. After 10 seconds the position of the aeroplane becomes E.

As

In ∆ABC

tan 60° =

we know tan 60° = √3

⇒ √3 =

It is given it is flying horizontally 1 km above the ground.

⇒ √3y = 1000 m

⇒ y = -------(1)

tan 30° =

we know tan 30° =

⇒  =

⇒ x + y = 1000√3

On substituting value of y from eqn (1)

x + = 1000√3

x = 1000√3 -

⇒ x =

⇒ x =

⇒ x =

⇒ x = 1154.7m

Since the distance travelled by aeroplane in 10 seconds is 1154.7 m.

As 1 hr = 3600 sec and 1 km = 1000 m

Therefore distance travelled by aeroplane in 1 hour = ⇒ 415.69 km/hr

Therefore speed of aeroplane is 415.69 km/hr

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