An aeroplane flying horizontally $1 \ km$ above the ground is observed at an elevation of $60^\circ$ and after $10$ seconds the elevation is observed to be $30^\circ$. The uniform speed of the aeroplane in $km/h$ is

$A$ ladder $5 \ m$ long leans against a vertical wall. The bottom of the ladder is $3 \ m$ from the wall. If the bottom of the ladder is pulled $1 \ m$ farther from the wall,how much does the top of the ladder slide down the wall?

$A$ flag-staff $5 \ m$ high stands on a building of height $25 \ m$. An observer at a height of $30 \ m$ observes that the flag-staff and the building subtend equal angles. The distance of the observer from the top of the flag-staff is:

$A$ ladder rests against a wall making an angle $\alpha$ with the horizontal. The foot of the ladder is pulled away from the wall through a distance $x$,so that it slides a distance $y$ down the wall making an angle $\beta$ with the horizontal. The correct relation is

$A$ tower subtends an angle of $30^\circ$ at a point distant $d$ from the foot of the tower and on the same level as the foot of the tower. At a second point $h$ vertically above the first,the angle of depression of the foot of the tower is $60^\circ$. The height of the tower is:

$A$ tower subtends an angle $\alpha$ at a point $A$ in the plane of its base,and the angle of depression of the foot of the tower from a point $P$ at a height $l$ meters vertically above $A$ is $\beta$. The height of the tower is