An aeroplane is flying at a constant speed,pa | vedclass

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

Question

(B) Let the height of the plane be $h = 5 	ext{ km}$.Let the positions of the plane be $A$ and $B$ at angles $15^{\circ}$ and $30^{\circ}$ respective

Vedclass · Accepted Answer

$720$

Vedclass · Answer

(B) Let the height of the plane be $h = 5 	ext{ km}$.Let the positions of the plane be $A$ and $B$ at angles $15^{\circ}$ and $30^{\circ}$ respectively.Let $O$ be the observer on the ground.In $	riangle ODA$ (where $D$ is the point directly below $A$),$	an(15^{\circ}) = \frac{h}{OD} \implies OD = \frac{5}{	an(15^{\circ})} = 5 \cot(15^{\circ})$.Using $\cot(15^{\circ}) = 2 + \sqrt{3}$,$OD = 5(2 + \sqrt{3}) = 10 + 5\sqrt{3} 	ext{ km}$.In $	riangle OEB$ (where $E$ is the point directly below $B$),$	an(30^{\circ}) = \frac{h}{OE} \implies OE = \frac{5}{	an(30^{\circ})} = 5\sqrt{3} 	ext{ km}$.The distance traveled by the plane is $d = OD - OE = 10 + 5\sqrt{3} - 5\sqrt{3} = 10 	ext{ km}$.The time taken is $t = 50 	ext{ seconds} = \frac{50}{3600} 	ext{ hours} = \frac{1}{72} 	ext{ hours}$.Speed $v = \frac{d}{t} = \frac{10}{1/72} = 720 	ext{ kmph}$.

Similar Questions

The angle of elevation of a point situated at a distance of $70 \ m$ from the base of a tower is $45^\circ$. The height of the tower is ..... $m$.

Two poles standing on a horizontal ground are of heights $5 \, m$ and $10 \, m$ respectively. The line joining their tops makes an angle of $15^o$ with the ground. Then the distance (in $m$) between the poles is:

The angle of elevation of a tower at a point distant $d$ meters from its base is $30^\circ$. If the tower is $20$ meters high,then the value of $d$ is

The upper part of a tree broken by the wind makes an angle of $30^\circ$ with the ground. The distance from the root to the point where the top of the tree touches the ground is $10 \, m$. What was the original height of the tree in meters?

In a triangular park $PQR$,$PQ = PR = 200 \ m$. $A$ $TV$ tower stands at the mid-point $M$ of $QR$. If the angles of elevation of the top of the tower at $P, Q,$ and $R$ are $45^o, 30^o,$ and $30^o$ respectively,then the height of the tower (in $m$) is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module