Question

An aeroplane flying horizontally 1000m above the ground, is observed at an angle of elevation

60
from a point on the ground. After a flight of 10 seconds, the angle of elevation at the point of

observation changes to 30
. Find the speed of the plane in m/s.​

Answer 1

Step-by-step explanation:

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Answer 2

The speed of the plane is 115.47 m/s.

Given

• aeroplane flying horizontally 1000m above the ground
• angle of elevation 60
• 10 seconds,
• the angle of elevation changes to 30

To find

• speed of the plane in m/s.

Solution

we are requested to find the speed of the plane which is basically the ratio of distance and time.

From the figure, consider triangle BCD

tan60 = DB/BC

or, √3 = 1000/BC

or, BC = 1000/√3

consider triangle EAC

tan30 = EA/AC

or, 1/√3 = 1000/AC

or, AC = 1000√3

now, distance traveled by plane,

AB = AC- BC

or, AB = 1000√3 - 1000/√3

We get,

AB = 2000/√3

distance traveled by plane = 2000/√3 m

time (given) = 10s

speed = distance/time

or, speed = 2000/(10√3)

or, speed = 200/√3 m/s

or, speed = 115.47 m/s

speed of the plane is 115.47 m/s.