A bird is sitting on the top of a vertical pole 20m high and its...

A bird is sitting on the top of a vertical pole

20m

high and its elevation from a point

O

on the ground is

45 °

. It flies off horizontally straight away from the point

O

. After one second, the elevation of the bird from

O

is reduced to

30 °

. Then the speed (in

m / s

) of the bird is A bird is sitting on the top of a vertical pole 20m high and its elevation from a point O on the ground is 45 ° . It

Options

A $2 0 \sqrt{2}$
B $2 0 \left(\sqrt{3} - 1\right)$
C $4 0 \left(\sqrt{2} - 1\right)$
D $4 0 \left(\sqrt{3} - \sqrt{2}\right)$

Correct answer

B. $2 0 \left(\sqrt{3} - 1\right)$

Step-by-step solution

A bird is sitting on the top of a vertical pole 20m high and its elevation from a point O on the ground is 45 ° . It

$AD = 20m$

$AO = \dfrac{20}{\tan 4{5}^{∘}} = \dfrac{20}{1} = 20m$

$CB = 20m$

$∴ BO = \dfrac{20}{tan{30}^{∘}} = \dfrac{20}{\left(\dfrac{1}{\sqrt{3}}\right)} = 20\sqrt{3}m$

$∴ AB = BO - AO$

$= 2 0 \sqrt{3} - 2 0$

$= 20\left(\sqrt{3} - 1\right)m$

It took $1sec$ to travel distance $DC$ .

$∴$ Speed $= 20\left(\sqrt{3} - 1\right)$ m / sec.

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