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Question

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.


Solution

AA´ and BB´ denote the height of the plane from the ground.

∴ AA´ = BB´ = 2500 m

From OAA´

tan 45o=AAOA1=AAOAOA=AA=2500 m

From OBB´

tan 30o=BBOB13=BBOBOB=3 BB=25003 m

Distance covered by the plane from A to B is AB or A´B´

⇒ A´B´ = OB´ – OA´

=(250032500)=2500(31=2500(1.731=2500×0.73=1825 m

Time taken by the plane in moving from A to B = 15 seconds

Speed of the plane

 =182515=121.66 ms1

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