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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

  • A bird is sitting on the top of a vertical pole 20 m high and its elevations 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
    `20sqrt2`
    B
    `20(sqrt3-1)`
    C
    `40(sqrt2-1)`
    D
    `40(sqrt3-sqrt2)`

  • A tower is 10sqrt3 metres high. If a point on the ground is 30m away from its foot, then the angle of elevation is

    A
    `45^@`
    B
    `30^@`
    C
    `60^@`
    D
    `75^@`

  • Two posts are just on the opposite side of a road. The heights of the posts are in the ratio sqrt3:1. The angle of elevation of the top of the smaller post from the mid point of the road is 45^@ . What is the angle of depression of the point from the top of the other post?

    A
    `60^@`
    B
    `30^@`
    C
    `90^@`
    D
    `45^@`

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