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A bird is sitting on the top of a vertic...

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is `45o` . It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to `30o` . Then the speed (in m/s) of the bird is (1) `40(sqrt(2)-1)` (2) `40(sqrt(3)-2)` (3) `20""sqrt(2)` (4) `20(sqrt(3)-1)`

A

`40 (sqrt(2)-1)`

B

`40 sqrt((3)-sqrt(2))`

C

`20 sqrt(2)`

D

`20(sqrt(3)-1)`

Text Solution

Verified by Experts

(4) `tan 30 ^2 =(20)/(20 + x )= 1/sqrt(3)`
`rArr 20 + x = 20 sqrt( 3)`
`rArr x= 20 ( sqrt( 3 -1) `
`Speed is 20 (sqrt(3-1)m//sec)`.
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Knowledge Check

  • From the top of a tower the angle of depression of a point on the ground is 60^@ if the distance of this point to tower is (1)/( sqrt(3) +1) metres , then the height of the tower is

    A
    ` (4sqrt(3))/(2)` metres
    B
    `(sqrt(3)+3)/(2) ` metres
    C
    `(3 -sqrt(3))/(2) ` metres
    D
    `(sqrt(3))/(2)` metres

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