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A bird is sitting on the top of a tree, which is $80 m$ high. The angle of elevation of the bird, from a point on the ground is $45 ° .$ The bird flies away from the point of observation horizontally and remains at a constant height. After 2 seconds, the angle of elevation of the bird from the point of observation becomes $30 ° .$ then the speed of flying of the bird is:

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26.28 m/s

24.28 m/s

27.28 m/s

29.28 m/s

answer is D.

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Detailed Solution

Given,
Height of the tree = 80m.
Angle of elevation from point of observation = 30°.
Angle of elevation from point on the ground =

45 ° .

Time taken by the bird to fly = 2 seconds
Consider the figure,
A bird is sitting on the top of a tree, which is 80 m high. The angle of elevation of the bird, from a point on the ground is 45 ^ ∘.

A bird is sitting on the top of a tree, which is 80 m high. The angle of elevation of the bird, from a point on the ground is 45 ^ ∘.

Let x is the distance between point C and tree. From

Δ A B C

find x.

x = 80 tan 45 ° ⇒ x = 80 m

We know that the distance covered by the bird can be represented as:

tan θ = height of tree distance ⇒ tan 30 ° = 80 x ⇒ x = 80 tan 30 ° ⇒ x = 803 m ∵ tan 30 ° = 13 ⇒ x = 80 = 803 ⇒ x = 803 − 80 ⇒ x = 58.56 m

We know,

Speed = \frac{Distance}{Time}

Therefore,

speed = 58.56 2 m / s ⇒ speed = 29.28 m / s

Thus, the speed of the flying bird is 29.28 m/s.
Therefore, option 4 is correct.

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