A bird is sitting on the top of a vertical po | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the initial position of the bird be $P$ at the top of the pole $PQ = 20 \ m$. The angle of elevation from point $O$ is $\angle POQ = 45^o$.In

Vedclass · Accepted Answer

$20(\sqrt{3} - 1)$

Vedclass · Answer

(B) Let the initial position of the bird be $P$ at the top of the pole $PQ = 20 \ m$. The angle of elevation from point $O$ is $\angle POQ = 45^o$.In $\Delta POQ$,$	an 45^o = \frac{PQ}{OQ}$ $\Rightarrow 1 = \frac{20}{OQ}$ $\Rightarrow OQ = 20 \ m$.After one second,the bird reaches position $P'$ such that $P'Q' = 20 \ m$ (since it flies horizontally). The angle of elevation from $O$ is $\angle P'OQ' = 30^o$.In $\Delta P'OQ'$,$	an 30^o = \frac{P'Q'}{OQ'}$ $\Rightarrow \frac{1}{\sqrt{3}} = \frac{20}{OQ'}$ $\Rightarrow OQ' = 20\sqrt{3} \ m$.The distance covered by the bird in one second is $QQ' = OQ' - OQ = 20\sqrt{3} - 20 = 20(\sqrt{3} - 1) \ m$.Since the time taken is $1 \ s$,the speed of the bird is $\frac{20(\sqrt{3} - 1)}{1} = 20(\sqrt{3} - 1) \ m/s$.

Similar Questions

$A$ person standing at a distance of $10 \ m$ from a pole observes that the angle subtended by the lower $\frac{1}{3}$rd part and the upper $\frac{2}{3}$rd part of the pole are the same. Find the height of the pole.

$P$ is a point on the segment joining the feet of two vertical poles of heights $a$ and $b$. The angles of elevation of the tops of the poles from $P$ are $45^{\circ}$ each. Then, the square of the distance between the tops of the poles is

$A$ tower of height $b$ subtends an angle $\alpha$ at a point $O$ on the level of the foot of the tower and at a distance $a$ from the foot of the tower. If a pole of height $p$ mounted on the tower also subtends an equal angle $\alpha$ at $O$,the height of the pole $p$ is:

$A$ man from the top of a $100 \ m$ high tower sees a car moving towards the tower at an angle of depression of $30^\circ$. After some time,the angle of depression becomes $60^\circ$. The distance (in meters) travelled by the car during the time is

An aeroplane flying with uniform speed horizontally $1 \ km$ above the ground is observed at an elevation of $60^{\circ}$. After $10 \ s$, if the elevation is observed to be $30^{\circ}$, then the speed of the plane (in $km/h$) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module