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Question

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. 


Solution

An aero plane is flying 1 km above the ground making an angle of elevation of aero plane 60°. After 10 seconds angle of elevation is changed to 30°. Let CE = x, BC = y, AEB=30,DEC=60,AB=1kmandCD=1km Here we have to find speed of aero plane.

The corresponding figure is as follows

So we use trigonometric ratios.

InDCE,

tan60=1x

3=1x

x=13

Again in ABE,

tan30=1x+y

13=1x+y

x+y=3

13+y=3

y=313

y=23

speed=distancetime

=y10sec

=231060×60

=425.68

Hence the speed of aero plane is 415.68km/h.

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