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 ......... $m/s$

A body of mass $2\; kg$ has an initial velocity of $3 \;m / s$ along $OE$ and it is subjected to a force of $4$ newtons in $OF$ direction perpendicular to $OE$. The distance of the body from $O$ after $4 \;seconds$ will be

A bomb is dropped from an aeroplane moving horizontally at constant speed. When air resistance is taken into consideration, the bomb

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. . . . .

If the time of flight of a bullet over a horizontal range $R$ is $T\, seconds$, the inclination of the direction of projection to the horizontal is

A missile is fired in horizontal direction from a height of $20\,m$ at a speed of $1000\, m/s.$ At what distance of ground will the missile land ?