Question

An angle of elevation of a jet plane from point A on the ground is 60 .after a flight of 30second ,the angke of elevation changes to 30 .if the jet plane is flying at a constant height of 3600root3m .find the speed of jet plane

Answer 1

Solution:-

Let A be the initial position of the plane above the ground and E be the position of plane after 30 seconds.

Let the speed of the plane be s m/sec.

Given ∠ABC = 60°, ∠EBD = 30°
& CA = DE
= 3600√3 m

Distance covered by the plane in 30 sec = s m/sec × 30 sec
= 30 s m
AE = CD
= 30 s m

In ΔBCA,
tan 60° = CA/BC
√3 = 3600√3m/BC
BC = 3600 m

In ΔBDE,
tan 30° = DE/BD = DE/BC+CD
3600 + 30 s = 3600 × 3
30 s = 10800 – 3600
= 7200
s = 7200/30
= 240 m/sec

Speed of the plane = 240 m/sec
= 240*80/5 km/hr
= 864 km/hr Ans.

Ans.) The speed of the plane is 864 km/hr.