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

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).

$A$ large tank is filled with water to a height $H$. $A$ small hole is made at the base of the tank. It takes $T_1$ time to decrease the height of water to $H/\eta$ (where $\eta > 1$),and it takes $T_2$ time to drain the rest of the water. If $T_1 = T_2$,then the value of $\eta$ is:

$A$ completely filled water tank of height $h$ has a hole at the bottom. The total pressure at the bottom is $4H$ and the atmospheric pressure is $H$. The velocity of water flowing out of the hole is $(\rho = \text{density of water})$

$A$ large open-top water tank is completely filled with water. $A$ small hole of diameter $4 \,mm$ is made $10 \,m$ below the water level. The flow rate of water through the hole is (Acceleration due to gravity $= 10 \,m/s^2$)

$A$ tank is filled with water to a height $H$. $A$ hole is made in one of the walls at a depth $D$ below the water surface. The distance $x$ from the foot of the wall at which the stream of water coming out of the tank strikes the ground is given by .............