The maximum range of a gun on horizontal terrain is $16 \,km$. If $g = \;10m/{s^2}$. What must be the muzzle velocity of the shell ......... $m/s$

Water is flowing from a horizontal pipe fixed at a height of $2\,m$ from the ground. If it falls at a horizontal distance of $3\,m$ as shown in figure, the speed of water when it leaves the pipe is $............\,ms^{-1}$ (take $g=9.8\,ms ^{-2}$ )

A ball rolls from the top of a stair way with a horizontal velocity $u\; m /s$ . If the steps are $h\; m$ high and $b\; m$ wide, the ball will hit the edge of the $n^{th}$ step, if $n=$

A ball is thrown from the location $\left(x_0, y_0\right)=(0,0)$ of a horizontal playground with an initial speed $v_0$ at an angle $\theta_0$ from the $+x$-direction. The ball is to be hit by a stone, which is thrown at the same time from the location $\left(x_1, y_1\right)=(L, 0)$. The stone is thrown at an angle $\left(180-\theta_1\right)$ from the $+x$-direction with a suitable initial speed. For a fixed $v_0$, when $\left(\theta_0, \theta_1\right)=\left(45^{\circ}, 45^{\circ}\right)$, the stone hits the ball after time $T_1$, and when $\left(\theta_0, \theta_1\right)=\left(60^{\circ}, 30^{\circ}\right)$, it hits the ball after time $T_2$. In such a case, $\left(T_1 / T_2\right)^2$ is. . . . .

A bomber plane moves horizontally with a speed of $500\,m/s$ and a bomb released from it, strikes the ground in $10\,sec$. Angle with horizontal at which it strikes the ground will be $(g = 10\,m/s^2)$