Beta Question Bank for Engineering: Mathematics>Chapter 14 - Heights and Distances>EXERCISE-1>Q 39

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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 $45 ° .$ 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

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Important Questions on Heights and Distances

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Beta Question Bank for Engineering: Mathematics>Chapter 14 - Heights and Distances>EXERCISE-1>Q 40

If the angles of the elevation of the top of a tower from three collinear points

A, B

and

C

on a line leading to the foot of the tower are

30 °, 45 °

and

60 °

respectively, then the ratio

A B : B C

is

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Beta Question Bank for Engineering: Mathematics>Chapter 14 - Heights and Distances>EXERCISE-1>Q 41

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point

A

on the path, he observes that the angle of elevation of the top of the pillar is

30^{°}

. After walking for

10 \min

from

A

in the same direction, at a point

B

he observes that the angle of elevation of the top of the pillar is

60^{°}

. Then, the time taken (in minutes) by him, from

B

to reach the pillar, is

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Beta Question Bank for Engineering: Mathematics>Chapter 14 - Heights and Distances>EXERCISE-1>Q 42

The angle of elevation of the top of a vertical tower from a point

A,

due east of it is

45 ° .

The angle of elevation of the top of the same tower from a point

B,

due south of

A

is

30 °

If the distance between

A

and

B

is

54 \sqrt{2} m,

then the height of the tower (in metres), is:

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Beta Question Bank for Engineering: Mathematics>Chapter 14 - Heights and Distances>EXERCISE-1>Q 43

Let a vertical tower

A B

have its end

A

on the level ground. Let

C

be the mid-point of

A B

and

P

be a point on the ground such that

A P = 2 A B

. If

∠ B P C = β

, then

\tan β

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 14 - Heights and Distances>EXERCISE-1>Q 44

P Q R

is a triangular park with

P Q = P R = 200 m

. A TV tower stands at the mid-point of

Q R

. If the angles of elevation of the top of the tower at

P, Q

and

R

are, respectively,

45 °

,

30 °

and

30 °,

then the height of the tower (in

m

) is