Height and Distance - Practice Questions & MCQ

 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 45⁰.  It flies off horizontally straight away from the point O.After one second, the elevation of the bird from O is reduced to 30⁰. Then the speed (in m/s) of the bird is :

Two ships $A$ and $B$ are sailing straight away from a fixed point $O$ along routes such that $\angle A O B$ is always $120^{\circ}$. At a certain instance, $O A=8 \mathrm{~km}, O B=6 \mathrm{~km}$ and the ship A is sailing at the rate of 20 $\mathrm{km} / \mathrm{hr}$ while the ship $B$ sailing at the rate of $30 \mathrm{~km} / \mathrm{hr}$. Then the distance between $A$ and $B$ is changing at the rate (in $\mathrm{km} / \mathrm{hr}$ ) :

If the angles of 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 30⁰, 45⁰ and 60⁰ respectively, then the ratio, AB: BC, is :

Which one represents the line of sight for the boat by an observer on the tower? 

An aeroplane flying at a constant speed, parallel to the horizontal ground, $\sqrt{3} \mathrm{~km}$ above it, is observed at an elevation of $60^{\circ}$ from a point on the ground. If, after five seconds, its elevation from the same point, is $30^{\circ}$, then the speed (in $\mathrm{m} / \mathrm{s}$ ) of the aeroplane, is :

The angle of elevation of the top of a hill from a point on the horizontal planes passing through the foot of the hill is found to be 45^o. After walking a distance of 80 meters towards the top, up a slope inclined at an angle of 30^o to the horizontal plane, the angle of elevation of the top of the hill becomes 75^o. Then the height of the hill (in meters) is

Two vertical poles are 150 m apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) is:

The angle of elevation of a jet plane from a point A on the ground is 60^o. After a flight of 20 seconds at the speed of 432 km/hour, the angle of elevation changes to 30^o. If the jet plane is flying at a constant height, then its height is :

$A B$ is a vertical pole with $B$ at the ground level and $A$ at the top. A man finds that the angle of elevation of the point $A$ from a certain point $C$ on the ground is $60^{\circ}$. He moves away from the pole along the line $B C$ to the point $D$ such that $C D=7 m$. From $D$ The angle of elevation of the point $A$ is $45^{\circ}$. Then the height of the pole is

A tower $\mathrm{PQ}$ stands on a horizontal ground with base $\mathrm{Q}$ on the ground. The point $\mathrm{R}$ divides the tower in two parts such that $\mathrm{QR}$=15m. If from a point A on the ground the angle of elevation of $\mathrm{R}$ is $\mathrm{60^{\circ}}$ and the part $\mathrm{PR}$ of the tower subtends an angle of $\mathrm{15^{\circ}}$ at $\mathrm{A}$, then the height of the tower is :