$A$ very large number of balls are thrown vertically upwards in quick succession in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is $5\, m$,the number of balls thrown per minute is (take $g = 10\, ms^{-2}$):-

The vertical height of point $P$ above the ground is twice that of $Q$. $A$ particle is projected downward with a speed of $5 \, m/s$ from $P$ and at the same time another particle is projected upward with the same speed from $Q$. Both particles reach the ground simultaneously,then:

$A$ ball is thrown up vertically with a certain velocity so that it reaches a maximum height $h$. Find the ratio of the times at which it is at height $\frac{h}{3}$ while going up and coming down respectively.

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at $4^{th} \, s$ after its fall and the next droplet is $34.3 \, m$. At what rate are the droplets coming from the tap? (Take $g = 9.8 \, m/s^2$)

Two stones are thrown up simultaneously from the edge of a cliff $200 \; m$ high with initial speeds of $15 \; m s^{-1}$ and $30 \; m s^{-1}$. Verify that the graph shown in Figure correctly represents the time variation of the relative position of the second stone with respect to the first. Neglect air resistance and assume that the stones do not rebound after hitting the ground. Take $g = 10 \; m s^{-2}$. Give the equations for the linear and curved parts of the plot.

An $NCC$ parade is moving at a uniform speed of $9\,km/h$ under a mango tree on which a monkey is sitting at a height of $19.6\,m$. At a particular instant,the monkey drops a mango. $A$ cadet will receive the mango if their distance from the tree at the time of the drop is $...m$ (Given $g = 9.8\,m/s^2$)