Water flows out of a hole on the side of a bucket and follows a parabolic path. If the bucket falls freely under gravity, ignoring air resistance, the water flow

If a small orifice is made at a height of $0.25\, m$ from the ground in a tank filled with water up to a height of $1\, m$,the horizontal range of the water stream will be (in $cm$):

$A$ cylinder of height $20\;m$ is completely filled with water. The velocity of efflux of water (in $m/s$) through a small hole on the side wall of the cylinder near its bottom is ....... $m/s$.

Water is filled in a container up to a height of $3\,m$. $A$ small hole of area $A_0$ is punched in the wall of the container at a height of $52.5\,cm$ from the bottom. The cross-sectional area of the container is $A$. If $A_0/A = 0.1$,then $v^2$ is......... $m^2/s^2$ (where $v$ is the velocity of water coming out of the hole).

The top of a water tank is open to air and its water level is maintained. It is discharging $0.74\,m^3$ of water per minute through a circular opening of $2\,cm$ radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to........ $m$

Consider the configuration of a stationary water tank of cross-sectional area $A_{0}$ and a small bucket as shown in the figure below. What is the speed $v$ (in $m/s$) of the bucket so that the water leaking out of a hole of cross-sectional area $A$ (as shown) from the water tank does not fall outside the bucket? (Take $h=5 \, m$,$H=5 \, m$,$g=10 \, m/s^{2}$,$A=5 \, cm^{2}$,and $A_{0}=500 \, cm^{2}$).