The angle of elevation of an aeroplane from a point on the ground is 45∘. After flying for 15 seconds, the elevation changes to 30∘. If the aeroplane is flying at a height of 2500 metres, find the speed of the aeroplane.
AA´ and BB´ denote the height of the plane from the ground.
∴ AA´ = BB´ = 2500 m
tan 45o=AA′OA′1=AA′OA′OA′=AA′=2500 m
tan 30o=BB′OB′1√=BB′OB′OB′=√ BB′=2500√ m
Distance covered by the plane from A to B is AB or A´B´
⇒ A´B´ = OB´ – OA´
Time taken by the plane in moving from A to B = 15 seconds
Speed of the plane