Question

An aeroplane is flying horizontally along a straight line at a height of 3000 m from the ground at a speed of 160 m/s. Find the time it would take for the angle of elevation of the plane as seen from a particular point on the ground to change from 60⁰ to 45⁰. Give your answer correct to the nearest second.

Answer 1

Given, AC = ED = 3,000 m

Speed = 160 m/s

In right ΔACB,

`tan 60^circ = "AC"/"BC"`

`=> sqrt3 = 3000/"BC"`

∴ BC = `3000/sqrt3`

`= 3000/sqrt3 xx sqrt3/sqrt3`

`= (3000 sqrt3)/3`

⇒ BC = `1000sqrt3` m

In right ΔEDB,

`tan 45^circ = "ED"/"BD"`

`=> 1 = 3000/"BD"`

⇒ BD = 3000 m

∴ AE = CD = BD - BC

∴ AE = 3000 - 1000`sqrt3`m

`= 1000 (3 - sqrt3)`

`= 1000 xx 1.268      ...(sqrt3 = 1.732)`

= 1268 m

∴ Time from A to E = `("Distance" ("AE"))/"Speed"`

`= 1268/160`

= 7.925 sec ≈ 8 sec