Q55 of 68 Page 9

The angle of elevation of an aeroplane from a point on the ground is 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of m, find the speed of the aeroplane.


Let D and E be the initial and final positions of the plane respectively.


It is given that BD = 1500√3 m


In right ΔABD, we have




⇒ AB = 1500


In right ΔACE, we have




⇒ AC = 4500


Now, Distance = BC = AC – AB = 4500 – 1500 = 3000 m


DE = BC = 3000 m


i.e. the plane travels a distance of 3000m in 15 seconds




= 720km/hr


Hence, the speed of the aeroplane is 720km/hr.


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