$A$ body falling from rest has a velocity $v$ after it falls through a height $h$. The distance it has to fall down further for its velocity to become double,will be $...............\,h$.

It is a common observation that rain clouds can be at about a kilometer altitude above the ground.
$(a)$ If a rain drop falls from such a height freely under gravity,what will be its speed? Also calculate in $km/h$ $(g = 10\, m/s^2)$.
$(b)$ $A$ typical rain drop is about $4\, mm$ in diameter. Momentum is mass $\times$ speed in magnitude. Estimate its momentum when it hits the ground.
$(c)$ Estimate the time required to flatten the drop.
$(d)$ Rate of change of momentum is force. Estimate how much force such a drop would exert on you.
$(e)$ Estimate the order of magnitude force on an umbrella. Typical lateral separation between two rain drops is $5\, cm$.
(Assume that the umbrella is circular and has a diameter of $1\, m$ and the cloth is not pierced through.)

$A$ horizontal bridge is built across a river. $A$ student standing on the bridge throws a small ball vertically upwards with a velocity $4\,m s^{-1}$. The ball strikes the water surface after $4\,s$. The height of the bridge above the water surface is $......\,m$ (Take $g=10\,m s^{-2}$).

An object is thrown vertically upwards. At its maximum height,which of the following quantities becomes zero?

$A$ body is projected vertically upwards at time $t=0$ and it is seen at a height $H$ at times $t_1$ and $t_2$ seconds during its flight. The maximum height attained is ($g$ is acceleration due to gravity).

Due to the presence of air resistance,if a body dropped from a height of $20 \ m$ reaches the ground with a speed of $18 \ m/s$,then the time taken by the body to reach the ground is nearly (in $s$)