Question

The angle of elevation of an airplane from point A on the ground is 60°.
After a flight of 10 seconds, on the same height, the angle of elevation
from point A becomes 30°. If the airplane is flying at the speed of
720 km/hr, find the constant height at which the airplane is flying.​

Answer 1

Answer:

Step-by-step explanation:

Let A be the point of observation on the ground and B and C be the two positions of the jet. Let BL=CM = h metres. Let AL = x metres.

Speed of the jet = 720 km/hr =720   m/sec = 200 m/sec

Time taken to cover the distance BC is 15 sec.

Distance BC = LM = 200  15 m = 3000 m

In ALB,

cot 60° =  

=  

x= ……………….. (i)

In AMC,

cot 30° =  

x+3000 = h

x= h -3000 ………………(ii)

From (i) and (ii)

h-3000 =

3h-3000 = h

2h= 5196

h=2598

Thus, the height at which the jet is flying is 2598 m.