Q. 454.3( 17 Votes )

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.

Answer :

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)


In ∆ADE


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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