Question

the angle of elevation of a jet plane from a point a on the ground is 60 degree . After a flighof of 10sec the angle of elevation changes to 30 degree if the jet is flying at a speed of 648km/hr find the constant hieght of jet plane

Answer 1

i think the answer for the question is 11664 root3

Answer 2

Let the site of the observer be A , the initial position of the plane be B and the final position be C

Now we make points B and C meet the ground at D and E respectively

clearly, BD = CE

Now, we need to calculate BC

Speed of the jet fighter = 648 km/hr = 648 x 5/18 = 36 x 5 =180 m/s

and time taken during this interval = 10s

thus, distance covered = speed x time = 180 x 10 = 1800 metres

Thus, BC = DE = 1800 m ------------ i

Let, BD = CE = h (say)

Now, in triangle ABD we have,

LBAD = 600 , LADB= 900 and BD = h

=> AD = h x cot 600 ............ ii

Again,

In triangle ACE we have

LEAC = 300, LAEC = 900 and CE = h

=> AE = h x cot 300 ------- iii

Now, AE = AD + DE

putting the values of AE , AD and DE from eqns.

iii, ii and i we have,

h x cot 300 = h x cot 600 + 1800

=> h √3 = h/ √3 + 1800

=> 3h = h + 1800 √3

=> 2h = 1800 √3

=> h = 900 √3 metres Ans

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