A lift starts from rest. Its acceleration is plotted against time in the following graph. When it comes to rest, its height above its starting point is

 

Two balls are projected from points $A$ and $B$ in a vertical plane as shown in the figure. $AB$ is a straight vertical line. The balls will collide in mid-air if  $\frac{V_1}{V_2}$ is equal to, 

In the given figure $AB$ is a pipe fixed to the ground at an inclination of $37°.$ A ball is projected from point $O$ at a speed of $u=20 \mathrm{m}/\mathrm{s}$ at angle of $53°$ to the horizontal and it smoothly enter the pipe with its velocity parallel to the axis of the pipe. Then length of pipe (in metre) is: (Take $g=10{ ms}^{-2}$) (Approximate the answer to the nearest integer.)

A particle is projected towards the north with speed $20 \mathrm{m} {\mathrm{s}}^{-1}$ at an angle ${45}^{\mathrm{o}}$ with horizontal. Ball gets horizontal acceleration of $7.5 \mathrm{m} {\mathrm{s}}^{-2}$ towards east due to wind. Range of the ball will be

(Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The figure shows three vectors $\overrightarrow{a},\overrightarrow{ b}$ and $\overrightarrow{c}$. Here, $R$ is the midpoint of $PQ$. Then which of the following relations is correct?