Question

angle of elevation of a airoplane from a ground is60 after 30sec angle of elevatipn of airoplane is 30 and airoplane of flying at contant height of 3000√3 than find speed of airoplane​

Answer 1

SOLUTION:-

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Given:

•Angle of elevation of a aeroplane from a ground is 60° after 30 seconds angle of elevation of airplane is 30°.

•Aeroplane of flying at constant height of 3000√3m.

To find:

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The speed of the aeroplane.

Explanation:

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We have,

Let A & D be the two positions of the plane & A be the point of observation.

It's given that angles of elevation of the aeroplane in two positions A & D from a point A= 60° & 30° respectively.

In ∆ABC,

• AB= h
• BC= R

$tan60 \degree = \frac{AB}{BC} = \frac{h}{R} \\ \\ = > \sqrt{3} = \frac{3000 \sqrt{3} }{R} \\ \\ = > \sqrt{3} R = 3000 \sqrt{3} \\ \\ = > R = \frac{3000 \sqrt{3} }{ \sqrt{3} } \\ \\ = > R = 3000m$

&

In ∆DEC,

$tan30 \degree = \frac{DE}{EC} = \frac{h}{R + M} \\ \\ = > \frac{1}{ \sqrt{3} } = \frac{3000 \sqrt{3} }{3000 + m} \\ [<strong>cross \: multiplication]</strong> \\ \\ = > 3000 + M = 3000 \sqrt{3} \times \sqrt{3} \\ \\ = > 3000 + M = 3000 \times 3 \\ \\ = > 3000 + M = 9000 \\ \\ = > M = 9000 - 3000 \\ \\ = > M = 6000m$

Now,

We know that, formula of the speed;

$\frac{Distance}{Time}$

So,

$= > Speed = \frac{6000}{30} \\ \\ = > Speed = 200m \: s$

Thus,

The speed of the aeroplane is 200m/s.