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 :

The angle of elevation of the top of a vertical tower from a point A, due east of it is 45⁰.  The angle of elevation of the top of the same tower from a point B, due south of A is 30⁰.  If the distance between A and B is m , then the height of the tower (in metres), 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 :