An aircraft is flying at a height of $3400\; m$ above the ground. If the angle subtended at a ground observation point by the aircraft positions $10.0\; s$ apart is $30^o$, what is the speed in $m/s$ of the aircraft ?
An aircraft is flying at a height of $3400\; m$ above the ground. If the angle subtended at a ground observation point by the aircraft positions $10.0\; s$ apart is $30^o$, what is the speed in $m/s$ of the aircraft ?
The positions of the observer and the aircraft are shown in the given figure.
Height of the aircraft from ground, $OR =3400 \,m$ Angle subtended between the positions, $\angle POQ =30^{\circ}$ Time $=10\, s$
In $\Delta PRO:$
$\tan 15^{\circ}=\frac{ PR }{ OR }$
$PR = OR \tan 15^{\circ}$
$=3400 \times \tan 15^{\circ}$
$\triangle PRO$ is similar to $\Delta RQO$
$\therefore PR = RQ$
$PQ = PR + RQ$
$=2 PR =2 \times 3400 \tan 15^{\circ}$
$=6800 \times 0.268=1822.4 \,m$
$\therefore$ Speed of the aircraft $=\frac{1822.4}{10}=182.24 \,m / s$
Similar Questions
What can be the angle between velocity and acceleration for the motion on a straight line ? Explain with example.
What can be the angle between velocity and acceleration for the motion on a straight line ? Explain with example.
A fighter plane is flying horizontally at an altitude of $1.5\, km$ with speed $720\, km/h$. At what angle of sight (w.r.t. horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target ?
A fighter plane is flying horizontally at an altitude of $1.5\, km$ with speed $720\, km/h$. At what angle of sight (w.r.t. horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target ?
A particle has initial velocity $\left( {2\hat i + 3\hat j} \right)$ and acceleration $\left( {0.3\hat i + 0.2\hat j} \right)$. The magnitude of velocity after $10\, seconds$ will be
A particle has initial velocity $\left( {2\hat i + 3\hat j} \right)$ and acceleration $\left( {0.3\hat i + 0.2\hat j} \right)$. The magnitude of velocity after $10\, seconds$ will be
Two balls are thrown horizontally from the top of a tower with velocities $v_1$ and $v_2$ in opposite directions at the same time. After how much time the angle between velocities of balls becomes $90^o$ ?
Two balls are thrown horizontally from the top of a tower with velocities $v_1$ and $v_2$ in opposite directions at the same time. After how much time the angle between velocities of balls becomes $90^o$ ?
The velocity of a body at time $ t = 0$ is $10\sqrt 2 \,m/s$ in the north-east direction and it is moving with an acceleration of $ 2 \,m/s^{2}$ directed towards the south. The magnitude and direction of the velocity of the body after $5\, sec$ will be
The velocity of a body at time $ t = 0$ is $10\sqrt 2 \,m/s$ in the north-east direction and it is moving with an acceleration of $ 2 \,m/s^{2}$ directed towards the south. The magnitude and direction of the velocity of the body after $5\, sec$ will be