Question

Angle of elevation of an aeroplane from a point on the ground is 60 degree after 15 seconds angle of elevation changes to 30 degree aeroplane is flying at a speed of 720 km/h . find the constant hight at which aeroplane is flying.

Answer 1

Answer:

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 × 5 / 18 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° = AL/BL

1 /√3 = x /h

x= h /√3 ……………….. (i)

In

AMC,

cot 30° = AM/ CM

x+3000 = h√3

x= h√3 - 3000………………(ii)

From (i) and (ii)

putting the value of x

h / √3 + h√3 = 3000

3h + h = 3000

_____

√3

4h = 3000√3

h = 750√3

and x = 750